There is nothing that will improve by you power cycling the SBMS instead of just turning the WiFi ON/OFF from the menu.
The old SBMS has the 4 buttons connected in a single row and the new one has them arranged as 2x2 that will be the easiest thing or check the diagnostic screen to see if is hardware 0.2 or 0.3
Has anything changed recently on the way you use the WiFi like on a different device or have you accessed the SBMS0. The original AT firmware is not that great but I have no control over that as it is made by the guys at espresif the people that produce the ESP32. The new SBMS0 version uses a firmware made by Robert that can work both as access point and as client and in client mode it should be more stable.
Are you connected at all times or you just connect to check the status from time to time then disconnect ?