Hi Emilian,
that error from BlueZ basically means that your adapter fails to
communicate with the device. This can have all sorts of causes, usually
related to chipsets / firmware / kernel.
Strategies I've seen working to solve it temporarily include re-pairing
the device or restarting bluetoothd, see e.g.
https://github.com/blueman-project/blueman/issues/650.
I doubt that it will be a major improvement as blueman is basically just
an interface to BlueZ in this case, but did you try a more recent
version of the blueman package yet?
On the other hand bluedevil is just a BlueZ interface as well, so it's
strange that it shows a different result. Can you confirm that you can
replicate that in both directions (connecting with bluedevil works, then
disconnecting and re-connecting with blueman fails vs. connecting with
blueman fails, then disconnecting and re-connecting with bluedevil
works) and provide the exact steps you take in both applications.
Keep in mind that using multiple bluetooth managers might cause issues
as well, though, as only one of them can have its agent registered as
the default.
Another interface you can try to test the steps is bluetoothctl.
Cheers