Thanks for sending those. I'm confused because in your original message, the namelist you provided goes from Feb 28th to June 1st, but the rsl.out.0000 file shows the case starting on May 30th. You also mentioned your wrfbdy file stopped at May 18th.
I also notice there is no integration happening on any processor except 0000. All other rsl files stop before it even starts integrating.
1) Can you share a namelist that matches the rsl files? If you need to run it again to get the right ones, do that first. To make sure you're only sending the rsl files for that specific run, it may help to remove all rsl files before you run wrf again.
2) Make sure the namelist you're sharing is the same one that was used to run real.exe.
3) Issue the following:
ncdump -v Times wrfbdy_d01 >& wrfbdy.txt
and then attach that wrfbdy.txt file, as well.
4) Please also attach your configure.wrf file (from the top-level WRF directory)
5) You may want to talk to a systems administrator at your institution to find out why only a single processor is doing the integration.