I can tell you that the crons did stop for a while (server wide it wasnt personal), but have been running for around a couple of hours now (in fact they restarted before I posted initially in this thread)
I know your jobs are running, ive seen them start up - hence the logs, but I do fear they may not be doing all you need them to, however, thats down to the script and thats beyond our general control.
I dont see why it wouldnt run manually, if you went to one of the URLS you have on cron the page would have run, in some shape or form, the effect may not be what you expected but thats down to the codeing of the page.
Imagine you had some airplanes waiting to take off
Plane1 4:13
Plane2 4:16
Plane3 4:20
at 4:20 your script runs and says "planes due at 4:20 should take off.." that only sends off plane3.. planes 1 and 2 get missed..
If they arent scripts you wrote, perhaps its a question for the script writers, what would happen if the cron job didnt run for a few hours