That size power supply should be fine. As these are modern chopper style drives, they won't actually draw the full 3.5A from the power supply unless you are really pushing all the motors hard at speed, which is quite unlikely.

It could however be a problem with the power supply. Ideally I'd connect an oscilloscope over the power supply, and see what is happening with all the motors connected.
You may be able to catch any dip in voltage with a voltmeter, as the dip would likely have to last for a second or two for the drive voltage to drop low enough to cause problems.
Does the power supply have any kind of voltage OK output? it may be worth connecting up a lamp to see if the power supply is shutting down when the problem happens.