Well, if you jailbroke it then installed a tweak, or something, you may have over used the system RAM, I did this on my 4s. I installed not far from 200 tweaks, it overloaded it so much i couldn't even open cydia to delete them, I did a restore but there were still issues, when the 5.1.1 update cam out, I did a full restore and update and things were fine, other than that you may just have some 'malware' which is apparently making its way round iOS currently, just try a clean restore up to 6.0 and hope for the best