Records for a second, then goes silent

Because the recording appears to continue, although silent, it rather suggests that whilst the sound device is correctly connected to Audition, the encoding part of it isn't doing anything - or at least that the information from it isn't being transferred to the temp file.

There are several things you can try, and should check, but also we need some more information. Mac or PC? Can you tell us what device class you are using if it's a PC? What version of the softare are you using? What sound device is it? As for things to try - see if there's an updated driver for your sound device, Just because it works with other software doesn't in iteself prove a thing, I'm afraid.

But initially, you should right-click on the Record button and make sure that it isn't in Timed Record mode, I think! It should be in Instant and Overwrite to behave normally.