QCII is a Motorola two tone format. For an individual call (two different tones) the timing would be one second of A tone, then three seconds of B tone. QCII group call (one tone) timing is 8 seconds of a single tone. Kenwood uses these timing parameters in their two tone decode ( although group will trip in five seconds instead of eight as I mentioned).
If your BLS rig only gets 3 seconds of a single tone to decode, this sounds like a old Plectron single tone scheme, not QCII. Although you can program any old tone freq into a kenwood, if it won't hold for five seconds at the least, it won't decode. The only way to change this would be to diddle the firmware, scary!