Almost every left chest that comes back looking wrong has the same problem, and it is almost never the machine. Someone scaled the artwork down, let the software decide what to do with the small text, and the letters closed up into a blob.
The arithmetic nobody does
At 4mm cap height, the stroke of a typical sans-serif letter is about 0.9mm wide. A satin stitch at the density most software defaults to — roughly 0.4mm between penetrations — puts four or five stitches across that column. Add the needle’s own displacement and the thread’s thickness, and the two sides of the column are physically touching before the design has even reached the fabric.
That is why the counter in an “e” disappears. It was never big enough to survive once thread thickness was accounted for.
Four things that actually help
Drop the density, but only on the small elements. Not globally. A 0.45mm spacing on 4mm text and 0.4mm everywhere else is normal. Global density changes are how you fix one problem and create three.
Switch to a run stitch under about 3.5mm. Below that, a satin column is pretending. A double or triple run reads cleaner, uses a fraction of the stitches, and does not fill in. It looks thinner on screen and better on the garment.
Widen the counters by hand. In an “e”, an “a”, a “g”, push the interior hole open by 0.2 to 0.3mm beyond what the artwork shows. It closes back up under pull-in and lands where the designer intended. This is fifteen minutes of nudging nodes and it is the single biggest difference between a hand-punched file and a converted one.
Use a centre-run underlay, not an edge-walk. On small text an edge-walk underlay adds bulk exactly where you cannot afford it. A single centre run holds the fabric without widening anything.
What to tell your digitiser
Send the fabric. A 4mm cap height that works on a woven oxford will close up on a pique polo, because the knit texture swallows the outline and the operator compensates by pushing density. If we know it is pique, we plan for it rather than react to it.
And if the logo has a 6mm tagline sitting under a bold wordmark, ask whether it should be there at all. Sometimes the honest answer is to drop the tagline from the embroidered version and keep it for print. Most clients end up with a dedicated embroidery version of their mark, which is what they needed anyway.