Thanks @DFScale. I hadn't heard of BQM, and it looks useful - but not for my present problem, because there's nothing wrong with the external internet connection: all devices connected by wire are working fine. It's only the WiFi that is playing up. Fortunately our house is riddled with rj45 socketry.
But I'm following the same principle - sending long sequences of pings to try to detect pattern in the dropouts.
I'll take your advice re IPv6, that makes eminent sense - thanks.

Another benefit of a replacement: the 7530AX supports Wi-Fi 6, while I seem to remember that the 7530 is only Wi-Fi 5. Tell Zen that the extra speed is very important!

Edited by cjn (Wed 08-Oct-25 00:08:54)

8.02 update was installed 4 Feb 2025

One thing the 7530AX won't do is be a mesh extender over WiFi. The 7530 will, so if you get the upgrade worth making the AX a mesh master and using the 7530 as an extender.

Thanks @partij32 for this. I spent a morning trying to set a pair of AX boxes as a mesh and failed. When I read this I used a cable but still had problems. After several hours of head scratching I found, although the cable worked for my PC, one of the connectors was damaged and it ran at 100Mhz not 1 Gb, so the Fritzbox refused to mesh. Replaced the connector and it now works great.

Returning to this... thanks for various comments since I was last here.
Trying to get more light, I turned on logging of Wireless device registration/deregistration, collected several days' worth of data, and exported them into a form where I can play with them in a spreadsheet (that was painful. AVM need some lessons on how to produce easily parsable log entries).
The results are revealing. Within the data collection period, there was one episode of WiFi problems. At that time, most of the devices connected to the WiFi were repeatedly being registered and deregistered; this was not associated with BandSteering or auto channel change logs (there were only a few of those, and no more during problem periods than normal). There were around 250 such events on the day of the problem, against about 50 on a typical day. Only in a minority (about 12%) of cases were devices logged as deregistering themselves, though the rate of this was four or five times normal; in other cases the devices were recorded as "was deregistered", presumably by the FritzBox. Other types of log report were around their normal levels during the problem period. That includes "The service provider successfully transmitted settings to this device", which has evoked suspicion in other threads on this site, though I'm still curious to know why it needs to happen 10-20 times a day.
I can't trace any unusual usage of the system around the time of the bad patch - both my wife and I were out of the house at the time, though our lodger was in - but she is not technically sophisticated so it's unlikely she would be doing anything different from usual.
For the moment the WiFi is working at a tolerable level. If we get any more episodes, I will report here in the hope that can help others, and start bugging Zen customer support for a replacement modem, preferably an AX in the light of comments above. Thanks to all for your advice, which has been most helpful.

In reply to a post by partij32:

One thing the 7530AX won't do is be a mesh extender over WiFi. The 7530 will, so if you get the upgrade worth making the AX a mesh master and using the 7530 as an extender.

My 7530AX (running 8.20) has a setting for both mesh master and mesh repeater. Only tried as master to 7530 and 3000 repeaters.

The latest beta firmware for the FritzBox 7530 contains a wif-fi fix for specific devices but may fix general droputs:

# Improvements of FRITZ!OS 8.10-125376 within FRITZ!Lab

## Wi-Fi:
- **Fixed** Connection problems with various wireless devices resolved, including Waipu TV Stick, NVIDIA Shield TV, Xiami 13T 5G, Sonos One SL, Lenovo Tab M11