To start off, I've ever only had one issue with a lever gun for this, and that was my fault.
I use a 92, a 94 an 86, or an 88 Winchester on occasion, and the last one is the one that almost let me down. On a typical second week deer hunt, where one day it rained, and the next was bitterly cold, i didn't dry out the rifle. So when the chance came, the only deer for the camp at the end of the season, it went click. The firing pin frozen. I waited, ejected the round, and tried again, this time with success. The deer was on the next ridge.
I've also carried a shotgun a very few times, and had success, but I've always figured it was too limiting, as the deer above would have walked.
The SMLE it of course a tough old bugger, but it's a heavy slug of steel when you are walking all day. (so is my 88 btw)
The SKS, a tad light IMO, but I have carried it, as i know I can use it within proper limits. Cracked the stock last year, so it now wears a synthetic.
The old 94 Winchester, what's to say? It's taken more deer for me, than all the other guys rifles in the old deer camp combined.
It's been both lucky, and durable, but even it is on it's second set of stocks.
The Remington semis, I've tried two, and both were jammers for me. Often they'd be flawless on the range, but jam in the bush. Too frustrating for me to own again.
Some day I want to have a go with another pump gun, I liked the old Remington one of our senior members (now passed) carried