Well, they may have to stop if they have trouble targetting and
focusing. If they’re using a multi-diode beam in order to avoid
high energy dispersion, the multiple beams have to converge, and it
is easier to focus if both you and the target are not moving. But
that’s just guesswork, if the software’s good, I don’t see any
reason to stop too.
Correction on the “can’t be intercepted”, heavy smoke or chaff
can hinder the beam.