My best guess from your description is that the new washing machine is discharging water at a faster rate than the old one, and this increased flow rate is causing the trap to siphon itself dry. With a relatively small pipe size like 1 1/2", and no vent to allow air to the back of the trap, it wouldn't surprise me at all if this is what is happening.
What I would do, if at all possible, is to change the drain line out to 2", and use a sanitary tee above the floor. Out of the side of the T install a 2" Ptrap with a riser of at least 2 feet to accept the discharge hose from the washer. Out of the top of the T install a vent riser that sticks up several inches above the washing machine. Install an air admittance valve on that to allow air to be sucked into the pipe to vent the trap.
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