I have two series slimline ballasts that will only light up one lamp. How could this be possible if they are in series? Judging by the inside wiring diagram of a typical series slimline ballast, this scenario can technically not happen...

Unless I'm missing something?

HF ballasts have resonance capacitors in parallel to the lamp, so if one of them fail short, it short out one lamp, keeping only the second lamp operating.

I have had the same thing happen with my magnetic series slimline ballasts as well. Too bad because they were nice early '70s Bonus Line ballasts. All of a sudden one lamp went out and the other glowed at probably 75% brightness. I haven't found an explanation for it yet either.

HF ballasts have resonance capacitors in parallel to the lamp, so if one of them fail short, it short out one lamp, keeping only the second lamp operating.

My ballasts are 60Hz magnetic though. 

I have seen this often also.  It is kind of a shame, especially since today's replacements are junk!

Maybe a short between internal ballast wiring?