Maximum time of exploring the wasteland and possible rewards
There seems to be no limit to the exploration time, some events occurr at 75 hours of exploration, but some player touched the 90 hours mark.
The level of the dweller does not matter for the chances at finding gear, but the S.P.E.C.I.A.L. do, because some fixed events are based on tests on the dweller S.P.E.C.I.A.L.; plus, as a rule of thumb, Luck always helps in finding gear and caps.
Generally the more your dwellers are out, the better gear they will find, even though there seems to be a cap of 1 legendary for expedition, and there is a confirmed cap of 100 items for expedition. After getting 100 items your dwellers will come back on their own.
(Note that this post was written early in the life of the game is likely out of date.)
In theory you can just keep reviving any explorer that dies in the wasteland to keep them out exploring indefinitely. I had an explorer out over 200 hours (more than 8 days) this way. However explorers can only carry 100 items, and they'll reach this limit long before that. With the latest patch explorers automatically stop exploring and start heading home once they reach 100 items, so it's no longer possible to have an explorer out this long.
Maximum Time Exploring
An explorer will collect 100 items after 3 to 4 days of exploring, so the current maximum time is about 100 hours. Since having higher stats means that the explorer will find more items, its actually the explorers with the lowest stats that can stay out the longest.
Maximum Time Without Dying
To maximize the time an explorer can survive in the wilderness without dying, you need three things. High hit points (HP), a high damage weapon and 25 stimpacks. To get explorers with the most possible HP you need to raise their endurance to 10 while they're still level 1. You then need to equip them with the outfit that gives them highest endurance bonus (ideally +7, but +5 is probably the best you'll be able to manage), and then start levelling them in the wasteland. Once they're level 50 and equipped with a good legendary weapon (20+ damage) they have a decent chance of surviving 100 hours in the wasteland without dying.
(Actually, sending them out before they reach level 50 can increase the amount of they survive in the wasteland. This is because levelling up restores the explorer's HP without using a stimpack. I'm not sure what the most optimal level is, but you can only do this once per explorer so it doesn't matter too much.)
Maximizing Item Quality
Length of time exploring does increase the quality of the items you'll find. However even after 200 hours my explorer was finding mostly junk. So it never gets that good. The one possible exception is a specific encounter that explorers will find after about 60 hours (2 days 12 hours) of exploring, the National Guard Depot. I've never gotten anything better than a "rare" blue item from this encounter, but others have reported getting legendary (gold) items from it. So you want to have your explorers out for a least 60 hours to have the best chance of getting the best items.
Recommended Strategy
At the start of the game, don't worry about any of this. Just send out explorers to get whatever stuff they can. Once you've unlocked endurance training rooms, fill them with level 1 dwellers and raise their endurance stats to 10. Then make those dwellers your main explorers. You should raise their other stats eventually, but once they've levelled up and you've equipped them with a good rare weapon (15+ damage) they should survive long enough to reach the National Guard Depot.
There doesn't appear any point of exploring beyond the National Guard Depot encounter. I always recall my explorers once they're past it. The sooner they're on their way back home, the sooner they can be sent back out for another chance at the depot. With the new limit of 10 explorers in the wasteland this is even more important.
So in other words, 60 hours is the amount of time that has to pass for you to get the bust stuff from exploration.
I've been testing various things. I currently have a dweller out for 105h 55min and she still has 5 stim packs. I go through a rather extensive training regime starting with training at level 1. I leave them in training until they are 10 in all 7 SPECIAL attributes. The endurance is most important because it seem to influence how many HP they get when they level up. Next I send them out into the wasteland for their alpha run which only lasts about 24h because they are so low level. It is important to give them a high endurance outfit to boost their HP when they level. When they come back they are usually near level 12-15. I heal them and send them right back out. This beta run will last much longer approaching 48h. I often cut it short when they are near level 30 which so far seem the optimal level for a max run. I need to test some at level 25 to see if that works any better. When they get back I have a dweller with the most HP I can give them, max SPECIAL stats, and at or around level 30. I give them the best weapon I have which right now is a hardened missile launcher (20-23), the best high endurance armor, and typically my best sphynx or husky variant to get them back sooner. They typically go for 48h without using their first stim pack by leveling up before they need one. After they hit level 50 they must rely exclusively on stim packs and by then encounters still do 2 dmg even when they succeed in killing it. They will kill behemoths (4000exp) but the 2 dmg will eventually whittle them down. Things I still want to test are different pets, the Abyssinian seem like it might help, I want to see if the DR reduces the 2 HP attrition. I doubt the pets that increase healing speed will help because dwellers don't have a healing speed while exploring.
Anyone know of pets that really boost wasteland survival time?
edit: One last observation, legendary dwellers are at a disadvantage because they start at level 20-35 and don't get the extra HP from having max endurance from level 1 up. I still keep them but they won't last as long in the wasteland. Yes, Colonel Autumn I'm talking to you, ya big pansy!