Not all machines can sew all fabrics, but I think I would loosen the tension, rather than tighten it. May be too tight and the thread's not able to stretch enough to hold a stitch. What thread are you using? Might want to try a heavier one.

Also you may want to invest in a Teflon foot,that will make the fabric move smoother thru the machine,or you could use tissue paper under the vinyl to make it move more smoothly.

Google,sewing on vinyl for more tips and tricks.
Kathi

Timing could be off, too. Timing a machine is usually fairly easy to do, but hard to describe.

Timing is messed up by simple things like needle in the wrong position too, or threading needle the wrong way. So (!!) easy to get wrong when going from one model to another.

Timing is all about the point when the over thread picks up the under thread, and the movment of all the parts for the two threads to meet at exactly the right spot. When this doesn't happen it skips stiches or they will not form at all.

Three layers of cotton napkin material is nothing for a 404. When it skips stiches it is usually threading, needle or some setup issue. This will mess up timing.

The first thing to check is correct threading and the way the needle is put in.

Second is a good clean up, as the years go by a lot of lint and muck can gather around the bobbin and the feed dog. Alwasy do a good oiling when you take out the machine.

For difficult vinyl it might help to use one of those leather needles with sharp knife like edges, but as long as the needle punctures the fabric with out working too hard, and the fabric moves fine over the feed dogs it's not a must.