I have recently converted a light fixture to 4x 13w 2pin PL  using robertson ballasts, model CC1320P ballasts, Something is happening that has also happened to me in the past with the same ballasts, after probably no more than 15-20 mins of being on, one of the 4 PL bulbs turns off, within a few minutes the others follow, after a few more minutes they turn back on one at a time in a within few minutes. does this have to do with overheating? the ballasts do get pretty hot, and if I open the fixture after it being on for a while it is surprisingly hot. are there any ballasts I could get online for decent price that behave better? I need four minimum. Also is it possible that this is caused by the bulbs?

If the ballasts have a overheating protection, this may occur.

I would assume the fixture and these ballasts were supposed to work along well, without any overtemperature tripping, so there is quite high chance the ballasts are actually dying and therefore overheating.
It could be the corrosion compromising the insulation between individual core plates, so the core eddy current losses are going up. The higher temperature also pulls down the flux saturation point, so the ballast start to operate at elevated current, increasing the losses even further.

Or even worse, the wire insulation becomes compromised among few turns. That would mean the ballast will die really soon.

Or the thing was designed to operate at lower voltage than you are using it at, 5V difference (115V vs 120V, or 120V vs 125V) is a lot here, it by itself (~5% change in the input voltage) cause roughly 15..20% power dissipation change (the slight core saturation makes the thing worse than plain (voltage ratio)^2, plus the fact the coil sees (even though phase vector-triangle) difference makes the coil voltage to vary percentage wise more than the mains voltage does) Or the lamp may exhibit lower voltage drop than the ballast is designed for.
So check the exact ballast ratings, if it matches what you have there as mains voltage and used tube.

Another factor that I think may cause the lamps to turn off and back on is due to the possibility of a severe voltage dip since inductive ballasts are extremely sensitive to variations in line voltage. For simple choke ballasts like the ones you shared here, the OCV is the same as the line voltage. I figure the arcs of those lamps may have extinguished due to the ballast’s OCV dropping below the level that the lamps require as a result of the decreasing line voltage. In that case, I recommend monitoring the line voltage that is being applied to your fixture using a volt meter.