2005 Chrysler Town & Country transmission stays in Park

I have a 2005 Chrysler Town and Country with 218000 miles, 3.3 L V6 w/automatic transmission. Trany rebuilt 48,000 miles ago with new solenoid. Occasionally , with the engine running, I put the shifting lever in Drive or Reverse or any other gear, and the transmission does not engage. It stays in Park. I return the shifting lever to Park and turn off the engine. Then I rock the van back and forth against the parking pawl several times and then start the engine. Then when I move the shifting lever to Drive or Reverse the Trany engages those gears. After several miles (30-100), the same problem occurs. Shifting lever moves to Drive or Reverse but trany does not engage. Once again I can rock the van against the parking pawl and Trany will engage. What could be the cause and how is it rectified? Can it be repaired w/trany installed or does the Trany have to be removed and disassembled? This is an intermittent problem. The gear shift lever always moves but periodically the Trany does not engage.

What happens if you put in low?

Happens in all gears. Thanks