Hi!
I also used to have the exact same issue with my T5 lights. I have a diy lighting system with four 39w high output tubes which are run by two Osram ecg ballasts. I googled your badboy and it looks very nice, the tube holders/fixtures (not sure about the proper name) look similar to the ones I use. And in them layed the problem in my case. The conections in there are made out off copper and since this fixtures arent moisture-proof (like the ones used in aquariums) high humidity causes them to oxidize even faster than normally. So basicaly, in my case the problem was a bad electrical connection between the light tube pins and the light holders/fixtures caused by corossion. To fix it I took the holders apart and cleaned the oxide of with a blade, scraped it of basically. Doesent hurt to do the same on the tubes pins.
Dont know if that is your problem but Im pretty sure that you have a bad electrical conection giving you grief. And I imagine that like in my system you have one ballast running two tubes so both tubes go out when there is a bad connection. They light up initally but because of tiny vibrations of the ballast the connection gets lost and they go out.
Check and clean all the connection points for those two tubes, but if your light system is still in warranty you may not want to take it apart.
This goes without saying, but here goes anyway, be sure to unplug it before doing any work on it. Better safe than sorry.
Hope you fix your problem.