A dedicated single shot may well have fewer parts to worry about breaking or wearing out. However, most of the single shots I've had experience with (Marlin and Savage) seem to be identical in every respect other than having a feed tray rather than magazine. My 2000L for example is basically a repeater with a plug with a feed tray built in. They even sold a kit that replaced that plug with a magazine. I've had no luck finding one though.
I've also never had a malfunction in a bolt action rimfire that wasn't ammo related (dud rounds). Most of the mechanical things likely to go wrong would be identical between a single shot and magazine fed bolt gun: firing pin or extractor. Either could eventually fail on any rimfire. Magazines may eventually fail, but are easily and cheaply replaced.
Stepping up to the mid range ammo, as opposed to the ultra cheap bulk stuff seems to be worth the price if going bang every time is a top priority. For example, with any of the rimfires I own (2 bolts, 2 semi's), I usually get one or two duds out of a 100 with Remmington Golden Bullets or Federal Champion. Not a big deal for plinking but not acceptable if it means losing a friendly match or shooting at food. With Federal Automatch, Green Tags, etc., I very rarely (as in I can't remember getting one) get a dud and notice fewer fliers.
The only mechanical malfunctions I've ever had on a rimfire have been with semi-auto's. Not saying they don't happen on bolt guns, just not as likely.