Plastic is probably going to be LDPE sheet in the .050"-.065" range.

I don't know what your part(s) look like or how many different ones
you have, but have you considered die cutting?

Maybe you do want a Kongsberg after all( http://www.esko.com/Web/site.aspx?p=579
), they are primarily knife cutters, the router spindle is sort of an
after though. We never cut LDPE on ours, but we did cut modified
styrene about that thick (even thicker with multiple passes) with a
knife blade The styrene is harder than LDPE, and was really a bit
much to knife cut, but the stuff had photographic prints laminated to
it and paper doesn't route well (but try telling the sales people
that)
An advantage to knife cutting is that there is virtually no kerf for
the vacuum to leak though and there is no place for parts to slide. On
the other hand small holes are a problem. The machines are expensive
though, but we had the "i-cut" version with an over priced optical
registration system (plus the router spindle was about a $20K
upgrade !), so a basic knife cutting machine would be a lot less than
the $150K I mentioned before.