In a small test scenario I'm measuring the signal strength at the AP.
Do the client smartphones keep a constant signal strength for probe
requests or are there reasons they are varying it?
The Question was not clear .Still below are the points i can tell from WLAN Technology.
In WLAN signal strength or RSSI keeps on varying as the medium is wireless.
Clients(Ex: Smart Phones) get RSSI of AP from AP's Beacon or any packets coming from AP.So depending on medium ,how that packet came to client ,client determines the RSSI and keep it for that time.
So coming to your question, there is no chance client gets constant RSSI/Signal Strength.
The Question was not clear .Still below are the points i can tell from WLAN Technology.