yeah, i had a similar problem years ago with my old surepower 410 from thermaltake. she lasted 6 years of hard work.
then started shutting down for no good reason. over time, i reduced the amount of items connected to the PSU and sure enough, it worked for a while but then carried on shutting down. in the end it was just board, hdd and graphics card, i had to disconect everything else.
grabed a new psu and was fine, but then i migrated my sims stuff to a smaller form factor PC my dad got me and now my only problem is too much downloads in my folder can casue my game to slow XD

(not the baby i play my online games on tho, that ones a custom hand built 8core *pats*) so yeah, it sounds like the PSU has started its journey to Silicon Heaven. if you never use the other drives like DVD ect, or other items, try disconecting those, and start saving for a newer PSU, thats how i eeked out the last life of my old thermaltake.