for some reason your cs5.5 was deactivated. if that was not an enterprise license, you can activate (for now) with the serial number.
before doing that, you might want to restart your computer and retry using a cs5.5 program. but if that activation prompt reappears, you have no option other than to re-activate using your serial number or you will not be able to use your cs5.5 programs.
p.s. in the not distant future the activation servers for 5.5 will age out and you will not be able to reactivate. that happened first to cs2, then cs3 and then cs4. cs5, cs5.5 and cs6 almost certainly will follow the trend.
We tried several times but activation failed (activation prompt reappears, keep loading) and now we could not use our CS5.5
I would like to raise that when we bought the CS5.5, there was no "reminder" that we would face this activation issue. So we should be able to keep using it as we wish. We are satisfied with functions provided by CS5.5 and need no additional functions. May I know if there is any way to solve our problem?
there's no way to use your cs5.5 beyond the trial period unless it's activated. there's no work-around and once the activation servers age-out, there won't be any way to activate cs5.5, at all.
that said, the activation servers for cs5.5 are still functioning so the problem is on your end. what that problem is, i do not know. a common problem is an adobe entry in the hosts file; check for that.
if that fails, if you have nothing else adobe on your computer, and if you have nothing to lose, you could:
1. (properly) uninstall your cs5.5 using the uninstaller(s)