Sounds like you might have a controller signal spiking issue.  If you are using rudder pedals, you can try disconnecting them before landing to see if the autobrakes work when the rudder pedals are unable to cause a spike while unplugged.  If this works, try increasing the null zone of the rudder pedals to about 15% to 20%.  A registered version of FSUIPC will smooth out controller spikes as well.