>Any ideas what this could be or what is causing it? I have at least one
>client that always receives this error in the activity log when it's
>session is backing up.

I don't think we've seen an ANR0444W with verb BeginTxn.
More context would help: client type & level; server level; whether this has
been a perpetual problem or started at a certain date...
Whereas it's occurring at the beginning of a transaction, it would seemingly
involve some negotiation/set-up values exchange, which may involve the client
password, transaction sizing, or perhaps compression settings.
I would have a look at the client backup log, and of course the dsmerror.log.
Sometimes issues like this come up with a great disparity in client vs. server
software levels.
I would do 'dsmc q opt' to see if any issue with the client options.  Look for
this having started after a certain options change or software change.
If necessary, perform a client trace to try to reveal supplementary info.
Any other, accompanying ANR messages in the Activity Log may be revealing.

  Richard Sims   http://people.bu.edu/rbs