AR-15s are somewhat like a beautiful, sophisticated woman: head turning, respected and admired, and very comfortable in your arms. They're also exacting, privileged and thirsty for exactly the right treatment from you. Granted that treatment, they'll function beautifully and reliably. Neglect yours too far, and it's likely to become temperamental.
Every good gun deserves quality care, so neglecting a bolt-action isn't condoned, but a disregarded bolt gun won't hold it against you. A quality bolt-action is like a good dog: forgiving, faithful and trustworthy.
Analogies aside, the reasons bolt-actions are almost unstoppable are these: They function through brute human force rather than by gasses bled off of a miniscule hole in the barrel. Factors vital to semi-automatic reliability, such as a bullet's dwell time in the barrel after passing the gas port; gas port diameter, action timing, mainspring strength and so forth just don't affect bolt actions. Apply as much muscle as is needed to get the job done, and keep shooting.
Furthermore, bolt actions have an incredible amount of camming power. Within reason, in a pinch you can force the bolt closed on a tight cartridge, whether caused by an out-of-spec handload, a foreign object in the chamber or whatnot. A similar cartridge, slammed into the chamber by an AR-15's speedy bolt, will stick stubbornly and refuse to allow the bolt to either rotate into battery or extract the stuck round.
That same camming power serves well when a fired case sticks in the chamber of a bolt action: Put what muscle is required into it, and you can usually crank that thing loose. Not so with an AR: A stuck cartridge is usually very stuck. I've seen frustrated shooters at the range literally pounding on the charging handle of their previously loved AR with a 2x4 in an attempt to get a stuck case — or worse, loaded cartridge — out of the chamber.
Back in my days as a big game guide in Montana, I saw multiple hunters put out of commission during the late season because their semi-autos (of various design) fell prey to icy conditions. Suffice it to say this: Cartridges with a thin layer of ice can't be forced to chamber in a semi-auto (they usually can in a bolt action); semi-autos with bolts invaded by ice often can't be forced to open (bolt actions can); and finally, a semi-auto rifle with a live round chambered, the bolt frozen shut and the safety frozen fast in the 'Fire ' position makes for a delicate hike back to camp. Yes, I've been there. Such conditions usually result in unprecedented abuse to the semi-auto in question — in an attempt to make it safe — before risking a long, dark trek back to camp through knee-deep snow.