If you set your Main Pedal > Midi Settings > Midi-Out > Sync > Disable your Infinity will not display the flashing midi sync light in the bottom right of the Infinity (as it does when the BB is set to Sync > While Playing).
Are you relying solely on the Infinity flashing light as the indicator for whether MIDI sync is working or not? If you have, reset both pedal settings to default factory settings and play with the connected pedals to see if pressing the BB pedal starts to play your loop back in sync with the BB. Long time ago I got an email from Pigtronix stating that updating or reinstalling the firmware resets the Infinity to factory default settings.
It seems like you’re now just throwing stuff on the wall to see what sticks and I know you have to be frustrated. Other users have provided pretty good advice on troubleshooting which is no more than identifying what is the source of the problem.
You will have to isolate and identify whether or not each of the component parts of your rig work as designed. Those components are the
- BeatBuddy (BB) pedal
- Singular Sound MIDI Sync Adapter
- MIDI patch cables
- Infinity Looper
To add just a little more to what BlueSkyIS suggested, you can use the steps from https://noterepeat.com/articles/pc-troubleshooting/794-using-a-midi-monitor-to-test-a-midi-device to identify which part is working. Before you start, I’d again suggest you reset the default settings on both the BB and the Infinity.
When problems such as yours happen, I usually start troubleshooting the cables. Sometimes easier to swap the MIDI patch cables when you have a spare.