I am curious because I did try making a $20 USD offer on one of those GE R80 uncorrected 1 kW mercury reflector lamps and the seller made a counter-offer of $150 USD. Will repeatedly making lowball offers kick someone off eBay?

I'm not sure. sometimes the seller has/will accepted really low offers. Case in point : I bought a 50w PSMH ballast that the seller had listed for close to $150 for $25 . WHY ? In this case the ballast had been listed for over 5 years . When I made the offer , eBay actually suggested I make a much higher offer saying the seller would be more likely to respond . I submitted the offer any way and won the ballast. My general rules of thumb for making offers on eBay are  1)- I check the "revisions" , if the item has been listed for a long time it might be worth a low offer. 2)- For normal instances , I won't offer less than the sellers original price as not to totally piss off the seller.  3)- If the seller has multiples of an item , check the "offer history" and see what offers have/haven't been accepted and go from there.  4)- Also if the seller has multiples , check how long it's been since the last item sold (just click on where it shows the number sold ) and use that to help make an offer.

 NOW , it is entirely possible to piss of either eBay or a seller with repeated low offers and get yourself into trouble so I wouldn't try to make a habit of it so just think before you offer !  

 I once had a car for sale and a potential buyer came up and immediately low balled me. I refused and he kept reoffering , increasing his offer by $100 each time. When he was within $300 of the original asking price he asked " What will it take to buy it" ?  My response was "For you ? NOTHING ! It's obvious you have the full amount with you but instead of making a sensible offer you decided to be a jerk so LEAVE !"  I then went back in the house !

You probably won't be banned from eBay itself but the seller might choose to ignore or block you if you anger them with repeated low ball offers.

I generally make offers around 10-20% off for most items I make an offer on. If I feel the seller's asking price is good though, I'll just pay their asking price. The exception to my 10-20% off rule of thumb is when an item is both 1) been sitting on eBay for over a year and 2) fairly overpriced meaning the seller probably overvalued their item.

I'm not sure what eBay will do about low ball offers. I would think nothing unless the seller reports you. Now I will say that I have blocked a buyer or two who made me low ball offers. Actually just blocked a buyer for that reason a couple days ago. Skipping to the end of the story, I told the buyer sorry I'm not going to sell you this item for $29.99 with free shipping when its gonna cost me $39 to ship it. Then I blocked them.

I'm not sure what eBay will do about low ball offers. I would think nothing unless the seller reports you. Now I will say that I have blocked a buyer or two who made me low ball offers. Actually just blocked a buyer for that reason a couple days ago. Skipping to the end of the story, I told the buyer sorry I'm not going to sell you this item for $29.99 with free shipping when its gonna cost me $39 to ship it. Then I blocked them.

Can sellers set offers to be automatically accepted or declined based on the seller setting the bottom limit in the auto system? I ask cause few weeks back I made an offer on something and the seller rejected it instantly in like a second. Wasn't a low ball to be a jerk kind of offer either but maybe too low for that guy. I did end up just hitting buy it now for that guy anyway.  Another seller I sent an offer to accepted it instantly upon submitting it.

Can sellers set offers to be automatically accepted or declined based on the seller setting the bottom limit in the auto system? I ask cause few weeks back I made an offer on something and the seller rejected it instantly in like a second. Wasn't a low ball to be a jerk kind of offer either but maybe too low for that guy. I did end up just hitting buy it now for that guy anyway.  Another seller I sent an offer too accepted it instantly upon submitting it.

Yes there is the option to set offers up with an automatic reject price, as well as an automatic accept price.

I believe they can . I've actually made offers that showed up as "Offer Accepted ! Pay Now!" literally the second I hit "Submit Offer" . No way the seller is that fast !

 BTW , when did the all of new smileys arrive ?

I believe sellers also have the option to send out offers to users that have either: added the item to their watch list, or have viewed the item at least 2-3 times.

The seller sent offers generally last for 2 days.

Yep ! I've gotten a number of them .

I believe sellers also have the option to send out offers to users that have either: added the item to their watch list, or have viewed the item at least 2-3 times.

The seller sent offers generally last for 2 days.

Yeah I do that a lot. Problem is most of the time when I send offers out, nobody accepts and buys the item. Some of my items are priced high but that's because that's what the items are going for. And with the effort involved with creating the listing, packing and shipping the item, then paying multiple fees, I like to not just give my items away. If I make no decent profit in the end then it's not even worth selling the item. Better off just tossing it in the trash.

Huh? You could get banned from ebay for low ball offers? I didn't know that...

Dunno if anyone's actually been banned or not.

I've never made a really low offer, but sometimes I'll make one a few dollars less, and seller make counter offer. If items are really expensive, I don't usually bother making an offer because I feel like they get offended and won't accept it.

I get though that packing and shipping stuff can be a hassle so they need to make something off the sale to make it worthwhile.

Yeah I don't sell my items cheap anymore. There's only a few items that I have marked down dirt cheap to get rid of. It's just not worth my time to go to my storage unit, get the item, bring it home, pack it, weigh it, ship it, then pay ebay about 10% plus a PayPal fee to only make a couple bucks. My time is worth more than that. That's why I've marked items up higher than what they used to be. I actually might just take the offer option off all my listings. That'll end the low ball offers for the most part. For the buyers who send me a message making a low ball offer I'll just ignore. If they want the item bad enough they'll eventually buy it for what I'm asking for it if they can't find it cheaper somewhere else.

You certainly wouldn't get banned for making a low ball offer on items for sale, but you need to think of how the offer will look to a seller and not offer them an insulting amount, especially when there is free shipping offered.
Try and find out how much it would cost to ship the item, and offer at least that amount.