Downloaded http://web.archive.org/web/19970215092459/http://www.musthave.com:80/OS2/ftp/pmp43.zip installed and it is running fine on ArcaOS.
I got that, and installed it on my Asus M3A78-EM quad core, in ArcaOS 5.0.3.1. I did not re-boot, I just started it, and a few seconds later, it froze the machine. The mouse won't even move.
I forced a reboot, and started it again. So far, no hang (and no DOSCALL1 problems), but it placed a lot of garbage over top of the bottom XCenter (and I do mean GARBAGE, the information is mostly useless). The XCenter widgets are far more informative, and take up a lot less room. I did not try to configure it, assuming that the most useful information would be default. There is probably some setting, that you are using, that is no longer compatible with OS/2.
I don't think the problem lies with ArcaOS. It is more likely that PM Patrol is just too old. I would be amazed if software that old, doing what it does, would not have problems (it is dated July 1996, after all). There have been a LOT of changes since it was written, and some parts may no longer be compatible with newer stuff in ArcaOS. ACPI, AHCI, and the modified kernel, would seem to be the most likely to be incompatible. None of them existed (in the current form), in 1996. I am also not so sure that CHKDLL32 is current enough to handle the job. PMDLL.EXE is included with ArcaOS, give that a try, and see if it tells you the same thing.