No matter what I do, I can't eliminate the occasional skip...

First thing, try a brand new needle.

Then after that, it's an elimination game...changing needle, thread, tension, etc.

Basic Maintenance Tension Skipped Stitches

Don Ignore Your Sewing Machine Skipping Stitches Simple Solutions

What to Do If Your Sewing Machine Is Skipping Stitches

Be sure to use a brand new needle. If the needle is bent or damaged, it will frequently skip stitches. Also, if you are using the incorrect needle for the fabric & thread you are using, it will skip stitches, ie a ball point needle on woven fabric.
All About Needles

Basic Maintenance Tension Skipped Stitches

What to Do If Your Sewing Machine Is Skipping Stitches

10 reasons for skipped stitches

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sounds like u have the wrong needle or machine is out of time. if its a needle feed machine u might have the wrong bobbin case. try lowering the needle slightly. machine is easy to time. theres a mark on the needle bar which u align with the bottom of the bar guide then loosen the hook (3 screws) and move hook till it just starts to meet the needle. careful of side to side movment. bobbin case has to remain in the finger.

Go back to the larger needle size. Bet you're seeing skipped stitches or crazy tension issues. Thicker stacks of fabrics need thicker needles. See also: http://www.gwsms.com/didyouknow.htm
http://www.picturetrail.com/sfx/album/view/17206792

lower your needle. If up to high can't catch the bobbin thread.

Skipped stitches
1. A bent or dull needle
2. The wrong needle for your fabric
knit fabrics require a jersey or ballpoint tip. Most wovens do well with a universal tip, and specialty fibers, like leather or metallic, usually require specific needles.
3. Incorrect machine threading
4. Unbalanced needle thread tension
Start by making relatively small changes and run a test stitch to evaluate the impact. If you need to adjust the tension dial using woven cotton fabric with good quality all-purpose thread and a new needle
5.check the needle is inserted correctly. The needle needs to be pushed as far up the needle shaft as possible. It's easy to insert the needle half way, clamp it down and think it is inserted correctly.
the flat part of the needle should be positioned towards the back. If the needle is not inserted correctly, it will not be able to pull up the bobbin thread and will cause skipped stitches.
6. If the suggestions don't help then it is time for a tune-up.

Skipped stitches means a bent or dull needle or improper needle for the fabric being sewn. Try a new needle of the correct type for the material being sewn. If this doesnt correct it, then it will be a timing or needle to hook problem and should go to a qualifed dealer for repair.

Your stylus is damaged or worn. Or some one may have spun the balancing weight at the rear of the tonearm. Reset the weight so that it will drop when two postage stamps are lain upon the stylus end of the arm.

if you adjust that setting, check that the needle goes into the needle plate the exact same distance front to back on both the right and left side. Also, be careful not to change the height when changing the twist.

First be sure you have a new needle in. A dull needle will cause this.
Also a burr from the needle having hit in the slot of the needle plate can catch the thread occasionally as well as a burr on the hook behind the bobbincase. With some very fine crocus paper or what is called a green stick these burrs need to be polished off. Or have them replaced. Check everywhere the thread touches. Otherwise it may be the timing is slightly off.