Here’s what we’re starting with: If it’s within 6 hours of your deadline, it won’t let you change it to be later. I.e., no snoozing your deadlines.
The 6 hour cutoff was suggested by 2 or 3 people and it feels like a good compromise between those of you who like the ability to snooze as emergency backup and those wanting to prevent akratic snoozing. (Straw polling suggests those camps are about equally represented.) Another proposal is paying to snooze, which is a cool idea, but probably too complex. We also like the idea of just-this-once snoozing, so you don’t have to remember to put the deadline back where it’s supposed to be the next day. But with this 6-hour snooze restriction that may not be much of an issue.
My only worry is that 6 hours is not very focal, ie, easy to remember. Like it’s the kind of thing that contributes to the feeling of beeminder being a morass of arcane, confusing rules. (: Or maybe you just remember “don’t try to change your deadline on an eep day” which you probably wouldn’t have expected to work anyway.
But @bee and I especially were abusing snoozing more and more so something had to be done!
PS: Here was my original beemail:
Bethany and I found ourselves insufficiently taking advantage
of arbitrary deadlines so we reduced the friction a bit by
making the deadline time under the countdown (above the
graph) be a link to the deadline setting.
Of course now we’re in danger of making it too easy to
snooze your deadline – ie, push it back as it approaches –
which Bethany and I are also both having a problem with. 
We’re inclined to do something overcomplicated like a
checkbox to abnegate snoozing, kind of like weaselproofing
yourself, and/or make snoozing be just-this-once, so that
tomorrow’s deadline is unaffected…
So, straw poll: What’s been your experience with deadline
a. I haven’t changed any deadlines at all.
b. I’ve customized deadlines but am never tempted to snooze them.
c. The ability to snooze is good as emergency backup.
d. I’ve akratically snoozed a deadline and would like to abnegate the ability.
(Also let me know if you hadn’t thought to snooze deadlines
but I’ve now put you on to the idea! In which case I may avoid
mentioning this in forum.beeminder.com until it’s less abusable…)
 I was supposed to send this beemail by 1pm and snoozed
it 5 times before getting it out the door by 3pm.