I recently had to attend a function in an auditorium. The place was fitted with 2xDuluxT/E downlights. When I arrived the lights were already dimmed very low and then ramped up because it was too dark with people walking in. I noticed one downlight din't work so I dismissed it as 'blown'. At some point the lights had to be turned off and when the video was over the lights came back on but this time the 'blown' one worked. Why is it relighted?

Many ballasts are designed so, when the control signal goes below the minimum dim level, they shut down completely. So when there become a need for more light, the control signal went up, so crossed theat shut-off threshold back, so the ballast restarted.
In many installations these partial shut down is programmed into the main controller, so it does not operate the lamps at too low levels, where they become inefficient and shut some of them down completely.

Some dimming ballasts have problem setting the correct dimming level

In most rooms in one of the college buildings there are dimmable 4x14w T5, there you often see one or two lanterns in the room that set wrong dimming level, or are out. I try to play with the dimmer and switch them on/off to "bump" them to the same setting as the rest but they respon eratically - They go out, if i try to start them into the dimmed setting they start and stay at full power and so on, after few hours i check again in that room and they appear to be fine....

Some evn "cycle" on their own when dimmed - The lantern starts from full brightness and dims down, suddenly 1 pair of lamps begins to dim more and the other pair brightens up, as the pair that dimmed extinguishes, the entire lantern "resets" and starts over dimming from max power....

And loks like the ballasts there "forget" to preheat the lamps sometimes in the dimmed setting as the death rate of lamps in that system is beyond any reasonable limits, and a few have noticable end blackening despite being fairly new

@Ash: That happen, when the ballasts do not have the minimum brightness level clamping and/or controlled shut down set correctly.
There would be all the time tolerances between the ballasts and all the lamps become unstable at too low level.

And I've seen many multi-lamp ballasts, where the lamp power balance between individual lamps was virtually not controlled on low setting, so even slight parameter imbalance cause one of the lamps to extinguish on way higher level, while the second still light somehow. In such condition the lamp circuit itself exhibit quite a large hysteresis, so any control scheme would lead to cycling at these low levels.
Such concept (without explicit balancing) is not able to go below 20% (with 5% tolerance on the output stage LC components and lamp arc voltages), but the controllers are frequently set to dim down to 5%. No wonder there are problems with that.

Other explanation could be, the ballast use voltage mode filament supply, but there is a wrong contact on some lamps. That mean the affected filament is not heated at low setting, so such lamp will tend to extinguish earlier and restart harder.
The short lifetime of the lamps would suggest this type of fault there... Because when the filaments are correctly supplied, no flashing and cycling of the ballast regulation could ever cause the lamps to wear out much faster than normal, full power operation.