Fired up the 5328A again and took a little more notice of things. It appears that it is at least being consistent and it would seem I have a gating problem.
Today's exercise has gone through four stages
* Gate doesn't open - reads zero (for somewhere between 15-30 minutes)
* Normal counting (for a couple of hours)
* Gate opens and doesn't close - counting just keeps running up and up and up (for 20 minutes, give or take)
* Normal counting (for a couple of hours so far... i.e. at the time of posting)
I'll keep running this for a few more days to confirm the pattern and then look at cracking it open at some point. Having it neatly secured in the rack makes this less appealing, especially when there are other things on my "To Do" list.