I have a rope washer that starts filled but then drains out

You will need to check you washer drain hose and make sure it is only inserted into your house drain pipe in the wall no deeper than 4-6 inches, alternately your house drain needs to be as high as the top of the washer lid. Be sure to secure your drain line from the washer to one of the water shut off fittings with a zip tie. You are most likely experiencing a siphon action because the washer hose is inserted too deep in the house drain. Pleazer Appliance...

check the drain hose. Is it in the drain below the fill line of the washer?
In other words -- the drain line should be above the level of the washer lid top and in the line about 4-6 inches

did you pull the spark plug out and clean it ? if you did , did you also put the starter cord and turn the motor over without the plug installed to get rid of the 2-cycle oil out of the cylinder ? if not do so.

Unless your unit is equipped with an easy start feature...and I think these are not, it is not usual to have to pull the trigger on the water gun to start one of these units. Also...if there is any chance that the washer has tipped over, there is a possibility that oil has gotten into the engine cylinder. Oil will not compress and the rope cannot be pulled..at all. Remove the spark plug and step back away from the exposed hole. Pull the recoil handle and watch for spraying oil from the spark plug hole. Pull a few more times, clean up the plug and the unit may start. If not, you may have to remove the carb bowl and drain more oil. Check your oil fill level. If your gas level is suddenly low you may have gas in the oil crankcase and need to change your oil. When the washer starts it may blow smoke for some time before it clears up.

Drain oil from mower until proper level. Remove spark plug and pull starter rope several times to blow out cylinder. Spray starter fluid in cylinder pull rope several times to clean out. Replace fouled plug with new spark plug. Remove air cleaner, ensure no oil present, replace filter as needed. Clean air filter box with carb cleaner. Install new air filter reattach filter cover. Prime engine, pull starter rope 1/2 way 4 times to help prime, then pull starter rope fully up to 10 times to start.

If the unit works when it is on the floor I would suspect three problems.
First make sure the unit is level using a bubble level checking left to right and front to back.
Second make sure the unit is securely on the dryer so when it spins it will not become unbalanced. You should see the washer spin slowly increase in speed and starting to violently shake then slow down again never achieving top speed if this is a problem.
The last possibility is to move the drain hose so it has a loop in it. Use a string, rope or hook it over something to hold the hose up so it will be at the height of the middle of the drum or higher and goes back down into the drain. Washers use a combination of a pump and capillary action to drain. This will also stop water seeping out of the hose when the drum is full allowing it to fill to full capacity.

It's in the drain hose somewhere,during the fill the water gets as deep in the drain hose as it does in the washer,during the wash the pump runs in reverse keeping the water level in the hose low,during the drain the hose is filled again.
Prop the washer up in front on a couple bricks or boards,start putting in water until it starts to leak and take a peak under the machine.

The water is siphoning out as it fills. Your drain hose is too low or has a air block. Remove the drain hose from the drain. Set the washer to fill. Hold the drain hose up higher than the washer. If it fills correctly and starts agitating,correct the drain hose problem.

Check you drain line. It may be too low or the air gap is blocked at the drain pipe.
A test is remove the drain pipe from the wall drain. Hold it up high and turn the washer on to fill.
If it fills and stops, then starts agitation. Repair the drain hose.

Drain the water. The item is probably in the pump/ filter