You may not be getting the whole picture. If anything (like errors) are sent to STDERR you will not see them in you log files. Try this command instead which will also redirect STDERR to the log file (note the end of the command):
rsync -av --delete /mnt/backup backupserverIPadress::backupfolder > /mnt/logs/textfile.txt 2>&1
You might want to also add in the --dry-run option. From the rsync manual:
This makes rsync perform a trial run that doesn't make any
changes (and produces mostly the same output as a real run). It
is most commonly used in combination with the -v, --verbose
and/or -i, --itemize-changes options to see what an rsync com-
mand is going to do before one actually runs it.
The output of --itemize-changes is supposed to be exactly the
same on a dry run and a subsequent real run (barring intentional
trickery and system call failures); if it isn't, that's a bug.
Other output should be mostly unchanged, but may differ in some
areas. Notably, a dry run does not send the actual data for
file transfers, so --progress has no effect, the "bytes sent",
"bytes received", "literal data", and "matched data" statistics
are too small, and the "speedup" value is equivalent to a run
where no file transfers were needed.