Hello,
i have made some screenshots to show my setup. Maybe it helps in reproducing the error. Done on my RPI4 with 2 GB RAM. I have uploaded them as a ZIP-Archive.

I create a new profile containing only the telescope simulator and the ccd simulator. Main telescope set to my 200PDS with 1000 mm focal length (actual 1009 mm resulting from plate solving).

ccd_config.jpg shows the setup of ccd simulator, simulating my Omegon 533 OSC camera.

site.jpg shows the Site Management for the telescope simulator.

plate_solve_config1/2/3/4.jpg show the configuration of the plate solver. This time i tried the "Local Astrometry". I have downloaded ALL index files 2Mass and Tycho2/Gaia - just to be sure nothing is missing....

As the first plate solver run takes more time I pointed the simulator to Polaris and did a simple Plate Solve with Action "Nothing".
The result can be seen in plate_solve_nothing.jpg. Takes little over 60 sec on my Raspi. I used 2x2 Binning, Gain 100 and 6 seconds exposure to show a little more stars in the simulation.

Then i started the Polar Alignment. Direction East, 20°. Plate solver needs little more than 4 seconds now. The Result of the first 3 alignment images is shown in polar_align_1.jpg.

I changed the Refresh rate (=exposure) to 6 sec and choose "Plate Solve". Then i hit the Refresh Button. Result is shown in polar_align_2.jpg - after more than 80 seconds i got multiple timeouts from the plate solver. Then i stopped the process....

I again pointed the simulator to Polaris and tried another solver. This time i switched to the internal solver and cleared the log area.

Again PA with 20° to East. First solve attempt took 49,64s. Mount slews. Second solve took 6.08s. Mount slews. Third solve took 4.72s. All fine. Again hit the Refresh button and the solver timed out. See polar_align_internal.jpg.

Maybe this is due to the modified settings for the plate solver during refresh? This maybe can lead to the first solve attempt taking much longer than the hardcoded 10s?

To avoid local plate solving on my "slow" RPi4 i changed to the online solver but this currently takes more than 10s and therefore is useless for the Refresh phase.

Next try with local ASTAP. First solve attempt with Action "Nothing" took 13.69s. I started Polar Alignment with this Solver. Again the first 3 images are solved without problems in less than 2s. But after Refresh a window showing the ASTAP progress pops up and shows polar_align_astap.jpg. Again: "Refresh solver timed out: 10.0s"

OK - back to the internal solver. Reducing number of stars by changing the exposure time to 2s and binning to 3x3 to hopefully speed up the solver. First "Capture&Solve" with Action "Nothing" took 6.9s. Looks good. See polar_align_internal_1a.jpg

Starting PA with 20° East again. No problems with the first 3 images. Solver solved in 4-5s. Should be fast enough for the Refresh phase. See polar_align_internal_2a.jpg

Hitting "Refresh" and i get "Refresh solver failed: 5.5s". See polar_align_internal_3a.jpg

Conclusion:

If the solver takes more than 10s, the Refresh phase does not work because of the hardcoded 10s limit in the refresh phase.

But: If the solver is "fast enough" i does not work because of unknown reasons... At least for me (and some others?). Less than 6 seconds should be enough - but for some reason the solver did not produce a solution.

I did another test on Merak in Ursa Majoris with the internal solver and 20° West, 2s exposure and 3x3 binning. The result is identical. "Refresh solver failed: 5.1s". And with Polaris with solver profile "Small scale solving". No success. And with "Single Thread Solving". Dito.

Then i reduced the field and search radius of the plate solver (Min Degree Width 0.1, Max Degree Width 1, Search radius 5) and tried again on Solaris with 30° East, 3x3 Binning, 2s exp. Same result: "Refresh solver failed: x.xs".

First step in a possible solution should be to add additional options in the solver settings to make it possible to change the hardcoded 10s interval - as it simply is not enough on slow machines like a RPi4 with small Memory (and not enough for the online solver).

Ciao, Udo