There are three main possible reasons why this could happen and this is what you can do to solve the problem:
1) FrostWire cannot fetch the Torrent file properly so the content won't even go to the Transfer list.
Our suggestion in this scenario is to try later, re-start the app or the internet connection and repeat your search or try to get the same file from a different source. Usually it will work with other sources if one fails.
2) Your Storage Location is set on SD card and you are running an older version of FrostWire (Prior or FrostWire 1.7.1 (build 232) on Android)
In this case highly recommend you to install very last version out of FrostWire. There is a version of FrostWire Basic on Google Play but FrostWire Plus is free too and will give you more results from cloud sources such as YouTube and SoundCloud so you don't have to get files only from Torrent sources.
This video will tell you how to get the last version of FrostWire Plus outside the Play Store:
3) Your Android device is plugged via USB to another device and Android unmount your SD card. FrostWire won't be able to save your downloads if the 'Storage Location' is pointing your SD card. Just unplug your device from the USB connection and you should be able to get the file you want to download on the Transfer list to download properly.
If the problem persists after running the last version of FrostWire and trying all the suggestions above it is possible a particular Torrent source could be broken or down (even for few minutes or hours), please send an email to firstname.lastname@example.org to report the issue so we can try to fix it.