Yorkie is completely right - the Gatwick Express brand has suffered even - I still feel the prestige element of the service has never recovered since the axing of the specially designed Class 460s...
The Thameslink franchise is seemingly a poison chalice for operators, and Govia probably, or should have, known that when entering it. Whilst the London Bridge works haven't helped things for GTR, their treatment of the staff has made things far far worse. If you want to get through disruption as smoothly as possible, and to run an effective service, you need your staff onside. It is rather blatant to see that GTR are at the complete opposite end of the spectrum in that respect.
I can't see the franchise stripped off them however - the Government is too preoccupied with other matters at the minute (well, one big matter), and unless they run into financial difficulties or things turn really sour, then I can't see it happening. The 700 introduction may appease some passengers, and things reliability wise should hopefully improve in the future. However staff relations are very weak it seems and will take a lot of work to try and repair...
I think a far bigger repurcussion for Govia is if they fail to retain the West Midlands franchise. That is a real possibility, with some worthy contenders; Abellio have been on the up recently and MTR a very attractive option. The latter certainly considering the fact they successfully delivered the London Overground operation, something that West Midlands Rail will be aiming to replicate.