I have a really rare incandescent lamp that's about 20 years old, and I hardly ever turn it on so it lasts longer. Unfortunately, something fell on it and left a tiny pen-tip sized hole in the glass. Is there anything I can do to extend the life now that the vacuum seal is broken? How many more burning hours can I expect it to last?
Maybe I can suck the oxygen out of the hole and seal it?

I'd just leave it as is and not power it up anymore. This will ensure the filament remains intact. Also be extremely careful with it because even though the chip is tiny, it greatly increases the chance that the glass could shatter completely as the chip creates a weak spot in the glass.
I'd take some photos of it ASAP just in case  it does break.

Hello,

There is nothing you can do about it. I assume its an incandescent lamp, the vacuum or more likely inert gas filling is done or detearating. The heat of running it will oxidise the tungsten filament and it will irreversibly demmaged and broken.

Theoridacally, if it is a vacuum incandescent lamp(wich most of today are not) it is possible to seal the hole and reevacuat it. However that is something extremely difficult, where special equipment and a very skilled and experienced glas worker is need, as well as clear knowledge about the glass used in the lamp as well as the atmosphere in it.

Due to the shock micro cracks might have formed in the glas, which can completely shatter the bulb when heated.

For very most lamp that is not a resonable choice. It is very often easier to source another lamp.


Best regards

Alex