TPControl opens a telnet socket on port 1319 to the NetLinx master, which the devices OS (and relevant WiFi driver) manage i.e. TPControl simply requests the OS on the device to open a telnet session, which remains permanently open as required for AMX ICSP requirements. If for any reason, TPControl detects that the telnet socket has closed, TPConrtol presents the 'Not Connected' dialog and every ~5 seconds automatically tries to reestablish the telnet socket, again by requesting the OS to open the connection.

So, there are a number of factors that can impact connectivity, but none that TPControl can influence/control. Besides the tests that you already appear to have tried (changing WAP/Router and associated Channel), we recommend that you review the available WiFi driver/firmware available for the device. Often you can find by Googling the specific part number and include "Wifi" you may see other people commenting on WiFi performance/problems.
But certainly, you should not notice any delay in feedback/operation (other than perhaps initial page/popup caching), when using TPControl on a device. Delays experienced likely suggests WiFi propagation/driver/quality problem.