1:18 online and 1:59 offline? What on earth-- Does it literally look and act like it's in slow motion? I can think of a few reasons that might happen, but not why it would stop when you go online.
CTRL+G toggles slow motion when in singleplayer (I think)
CPU usage being maxed out can cause rF2 to stop running in real time, and be forced to slow down.
Some controllers need you to open your controller.ini file and set 'Skip Updates' to 1.
Are you running with AI when you practice in single player? Even if you're in a private session, overwhelming your CPU with AIs might explain it.