Depending on the signal you are listening to, some amount of static/broken reception (aka Picket Fencing) is to be expected..
But, if it's really bad, then you likely have a loose connection in your coax connectors or the antenna mount, etc. You say the connections are tight but also make sure the antenna is not loose on the mount (if it has a screw-on mount).
It could also be worn/broken coax. IIRC, the coax..actually more like a thin wire, that comes with the MXT400 is VERY thin and is not very durable.
I suppose it is also possible that there is a loose connection inside the radio, but IMHO, that is less likely..
are you sure it's not just regular picket-fencing of a weak signal? If it happens to even very strong signals, then something is loose/worn.