I'm no rocket surgeon - but I'd bet a bag of pucks: sticky/worn-out microswitch under your "stop" button.
This happens with many/most MTR's, not just Tascams...it's common 'cuz those transport buttons (especially "play" & "stop") are used 50x more than any other control on the panel.
I've heard of tech-nerd/gear-hawrs who manage to get to the microswitch and clean it, De-Oxit it, even replace it. I'm not quite in that league...I'm more likely to sit in the corner and cry uncontrollably...