Hi, as it's only the X axis that is moving I would "guestimate" that you have a way oil cushion build up that is pushing one side of the X axis dovetail away.....as soon as the motion stops the oil build up drains away.......you could try a thinner way oil........perhaps the seals at the end of the X axis dovetails are allowing this to happen......remove the seals at one end and see what happens.
A moving body with a fluid between it will "aquaplane" when the body is in motion.....it's called dynamic something or other.......can't remember the exact term.
If the forward motion is slow the pressure dissipates but with fast motion you get a denser layer between the 2 surfaces that will create a pressure.....having slack gibs will exacerbate the problem......thjs will create a void for the pressure to move the slides back and forth.
Do a test........with a dial indicator against one end of the table.....grip the table on the ends and attempt to rock it sideways against the dovetails......the dial indicator could move a few thou but if it moves a lot the gibs are too slack.
Slack dovetail jibs are one solution people use on a manual mill retrofit to overcome dovetail friction and stepper motor stalling......one reason why linear rails are so good in that concept as they work practically metal to metal without jamming up.
If this pans out to be the cause, you might need to have a more powerful stepper motor or servos to move your axes.....slack gibs are NOT the way to go......maybe thinner way oil.
Ian.