I know this has to have been asked a million times, but I can't find any post relating to why the GOG version has a time limit of 150 days, even though it's patched to v1.2, where v1.1 was supposed to extend that to 500 days.

Am I wrong about this? Is there a setting, patch, or some sneaky method to extending the game time? I've only played for a few hours and much to my dismay, have lost almost 50 days already!

If it's any help, I've played for years and never hit the second, "stop messing around" time limit.
Glad you figured out your trouble! Have fun!

Also, there's a way to increase some time. Go to The Hub. And bring some caps with you (3-5k must be enough, I think. It's been some time since I played Fallout 1).

No real reason to waste the money you will be hard pressed to use up the intial 150 days before solving that quest.

You could use that time to train up stats that affect levels, such as Intelligence, Endurance and Strength.
Just sayin'. I was able to become a Brotherhood of Steel member, up my Intelligence and still get stuff done in 150 days. I'd been avoiding levelling until I'd got those stat boosts, mostly.

Unless it's his first time playing, in this case it's better to have more time to explore/solve quests/do whaterever he wants. At least I don't like having to rush to finish the main quests (one of the reasons why I like Fallout 2).