I really think there should be more time than two minutes to pick up eggs, more so because of seasonal hunts.
I ended up losing a Uilus egg because I had to go do something else for a couple minutes (refreshed page, went to bathroom, came back, saw egg, clicked and saw the error alert).
It might be my fault for not checking before leaving, and I am a little bitter, but two minutes for a limit is a bit short, especially when you may be distracted by something for a short while.
I'm not asking for three hours or anything, maybe five minutes rather than just a measly two. Hopefully, I'm not the only one who has these feelings.