"why don't most people just stay in that trade till it goes back up? "
Because they want to make money fast, like Timothy S, who made a fortune buying/selling penny stocks in a short period of time.
"Is there like a time limit for how long you can hold a trade?"
No, as long as you buy it with cash. You need a margin account to short stocks and you're required to maintain certain % of cash when you buy/sell penny stocks on margin. I don't think some brokers would let you short pink sheet (penny) stocks, it's not even profitable for them.
If you buy something and it keeps dropping in price, it will likely to consolidate for a while, at least 3 months, before going back up again. But it's quite unlikely the price will be the same as to where it started dropping. Something that is worth a penny won't be worth a million in the future, this is how finance works today.