From what I have experienced (and as our tutor has often told us!) commonest reasons for speeding up are:
Letting runs of quavers go into "free fall"
Not holding dotted notes long enough
Not holding long notes at ends of phrases long enough before going into the next line (the latter often applies to singers too, who can't cope with "spaces" or hold a note its full length.

And (shoot me down in flames!) certain instruments - played tucked under the chin with a bow - or rather, their owners, tend to be the most likely to run away with things, tho' a couple of moothie players at one of our recent sessions got a severe telling off from the session host!