Generally, I like the current mission timers, which give an urgency to your actions. However, I understand the OP. I've failed a few missions due to RL time limits and I hated it.
I'm not sure if some missions are "special" or the mission system changed, but I once missed a deadline (a long time ago), while I wasn't logged in, and when I next played, I was surprised to see that I'd been given another 24 hours to complete the mission, for a reduced payout (according to an in-game email in the comms panel).
It would be nice for something like that to be available for regular missions: Extend the mission deadline (when possible, due to mission type), so when you log back in, you get another 24 hours, with a "regretful, but we still need it" email and lowered payment and faction status improvement. Maybe even a 7 day extension with a significantly lowered reward and faction status is unchanged (didn't go up, but since you eventually achieved the mission goal, it doesn't go down either - or only drops a little).
I think this would fall under the category of a QOL improvement.