After a couple of seconds they would be able to continue as if nothing was amiss.
The tac_plus (I am using the Event-Driven version) logs were not showing anything out of the ordinary so this was a rather perplexing issue. The error seemed to be popping up rather randomly (and always when I did not have a tcpdump running).
While observing several devices over a larger time period I noticed that they were experiencing intermittent packet loss and this got me to wonder of the packet loss events I was noticing were not coinciding with the authorization failures.
Lucky for me tac_plus is running on a Linux host and so I thought I'd simulate packet loss between one of my own devices and the tac_plus service to see what that would result in. To implement the simulated packet loss I simply put the following rule in place:
iptables -A INPUT -m static -mode random -probability 0.5 -s /32 -j DROP
With a probability of 0.5 (this can be between 0 and 1) I was dropping around 40-50% of the packets.
Lo and behold, '% Authorization failure', scientifically reproducible.