Is the reason the soloist is often silent during a Baroque-era concerto simply to provide a break from all the virtuosity often required within the outer movements? Or is it to allow a string soloist to quietly retune?
As I do my listening today and come across a Baroque-era concerto in which the solo instrument is silent during the slow movement, I will certainly post the info on that recording here
I think what you'll find is that this happens only when the solo instrument is a natural horn or trumpet. While it is possible for these instruments to be used in keys other than the instrument's own key, this capability was rarely if ever used in the baroque period. Slow movements are often in a contrasting key, making it difficult or impossible for the solo instrument to play (under the norms of the time).
Furthermore these movements are usually not only slow but also quiet and peaceful. Horns are traditionally instruments of the hunt, and trumpets of military and stately occasions. They are loud, and their idiom is full of energetic leaps, scales, dotted rhythms, and triplets. Yes, there are exceptions to this rule, but a typical concerto is going to exploit the idiomatic style of the instrument, so most horn and trumpet concertos of the Baroque period will give the soloist a rest in the quiet movement.
Strings and winds, by contrast, have both energetic and languid idioms, and they don't have the difficulties of horns and trumpets playing in contrasting keys, and in fact you will find that they typically do play in the slow movements of their concertos.
Found one! The Vivaldi Concerto for Two Trumpets in C Major, RV 537. A performance on YouTube with a Japanese ensemble.
See what I mean?
Also note that this slow movement is 6 measures long, which could be motivated by the need to provide a bit of contrast without boring the soloists. (But slow movements like this are far from rare in baroque concertos and sonatas.)
This slow movement calls to mind another factor, affecting trumpets particularly, which is that the fourth and seventh degrees of the scale are rather far out of tune compared to the diatonic scale. Modern "natural" trumpets have ahistorical finger holes to compensate for this, but in the baroque period there was only the player's technique: lip tension, breath pressure, and embouchure. In a fast movement, the notes are short enough that slight inaccuracies of tuning will be less noticeable. In a slow movement, this is not going to be the case. In this Vivaldi concerto, for example, the first violin part of the slow movement entirely comprises notes that are available to the natural trumpet. But the F is likely to be out of tune and/or have a different tone because of the pitch bending. That will have a minimal impact on a note lasting a quarter of a second, but a major impact on one lasting four or five seconds.
Most string and woodwind soloists do get parts in slow movements. Brass players, especially trumpet players, need to rest their lips a bit now and then. Bach's Brandenburg Concerto #2 is an example. (There are exceptions.)
Horns and trumpets were valveless so non-harmonic notes required differences in lip position and air pressure.