they never expire. Shorts have no time value on them (apart from the daily interest they are paying for it).
Eli5, Melvin borrowed shares that may or may not exist and introduced them into the marketplace hoping the over supply will kill prices. It turns out their thesis was false. and people kept buying up the supply.
Every day those short shares are on the market, they pay interest based on that day's closing price. This is a very important point. because let's assume they were paying 3.6% annually (this number will make more sense soon) when they opened it at $4. And let's assume for simplicity's sake, they only opened 10 short shares. their max profit on those short shares would be if GME went into bankruptcy and they never had to buy those shares back. so they could have made a total of $4/share.
usually, interest assumes there are 360 days in a year, so 3.6% annual interest means they are paying 0.01% interest per day. at $4, they would have been paying 0.04 cents a day per share, or 4cents in interest every 10 days for their total of 10 shares. Again, for these 10 shares, the absolute most they can make is $4/share or $40 if GME goes into bankruptcy (minus the interest they pay).
Now let's assume GME can rally to $400 by close today. For today alone, they will owe 4 cents per share. As you can see, even though the short shares never expire, they start paying hefty fees on them, which will eventually cause them to either decide to keep waiting or finally close.
Technically speaking, if they are willing to pay the exorbitant fees forever, they could technically hold those short positions forever. So they could try and play a game of chicken and see if we blink first. or just admit defeat and close it early.
Also note that short shares are bought on margin. i.e. you need to prove to your broker that you can actually make them whole again by buying shares back. So if my total assets were only $4k before, and the cost to buy back all those shares now at $400/share is now $4k, my broker could go "dude, we gave you your chance, even though you can keep paying these fees, you can't afford to buy those shares back at these prices. We aren't going to risk our money so you have to close your position now."