Did you check if /tmp/ is really read-only when that happens? If it is, you need to find out why. I don't know how x2go could make it ro, so there's likey a different reason for it.
/tmp is on root, and does become read-only. So does everything else on the root partition. And thus nothing works.
I somehow suspect that the files x2go creates on /tmp might be causing the errors which make the root remounted as ro. I have not had this problem before I started playing with x2go. I am not sure how to debug this, but I will try when this happens next time and report.
Thanks