I've done a few solo trips. One stands out not so much for the length as for the utter aloneness.
In 2010 I spent most of the summer at a lodge in the Alaska Range. Sheep season opens on August 10th, with most hunters arriving in the field on the 8th or 9th. The weather was lousy that year with high winds and rain/fog stranding hunters, guides, and clients at their jumping off points on both sides of the range. I "clocked out" of my job on the 8th and was sitting on the lodge porch with a loaded pack, watching the rain, pretty much like everyone else within 100 miles.
Then on the afternoon of the 9th, the weather broke very briefly. The pilot picked me as the first flight out and we made a run into the mountains. He kicked me out on a gravel bar strip I'd never been too before, and 30 minutes later the fog rolled in and I was as alone as it's possible to get.
Life consisted of rain and rocks for the next four days. No other hunters made it into that part of the range, and I never even heard another cub until the clouds lifted on the fourth day and I met the pilot back at the strip.
Hunting- 9 days on elk in the Uinta Mountains in Utah.
Hiking- this year I'm doing a solo 21 day 211 mile thru hike with two re-supply caches in the Sierra Nevada Mountains. But I guess this doesn't count as I'm not hunting. Sorry.