I have gone 3 for 20 on starting seeds using various methods: paper towels, root riot, peat pellet, all with a sprouting heat mat. I get a small tap root, 1/4 -3/8" that is tight to the seed body then it stops. Seeds are from 2 different stores. All of my tomato seeds that were next to them did great. It has got to be something i'm doing. Thanx in advance.
YO dude, only potential tip i can offer is that in general the initial taproot only tends to stop growing if it's sitting in too much water, as it's got no reason to explore - it sounds like you're soaking them well enough to get the initial shell crack, though after cracking it helps to allow paper towel/medium to dry out abit so taproot is encouraged to grow out searching for water - i soak my medium thoroughly pre-pop then just keep it slightly moist-to-dry after the pop.
Also if seeds remain sitting in too much water after pop, then they're much more prone to rot & die - the taproot should ideally always be a bright a white as possible, and though slight yellowing is not the end of the world, once it goes browny/yellow then it's dead & gone. If you're seeing the little tails all shrink & start browning off, then sitting in excess water is usually the cause.
IF not sitting in too much water, then only possible other explanation is they don't like something about your water - most likely culprit is always chlorine & chloramine, as little taproots really hate it, and that could explain why you're seeing same results over different mediums. Water Temperature is also important, as too cold can cause root shock, especially if the medium is already heated, though tbf Temp alone is unlikely to kill them, it'll more just stunt their growth only. pH isn't so important until you've actually got a root zone going, though maybe also check if possible that your water isn't wildly alkaline or acidic, as crazy pH numbers would still cause damage & death to little taproots too.
There's always the possibility you've just got duff or old seed stock, but normally dud seeds just won't pop full stop - if they're all popping ok but then dying with little tails poking out, that's likely to be an environmental issue, not age or genetics, etc.
Regarding paper towel method only, I have also had issues with using certain toilet roll & kitchen towels, as alot of the more expensive brands often have some sort of coating or chemical infusion. I've previously found some seeds just didn't seem to like the paper they popped in, and using just cheapo, basic, school type paper towels was the best. Again though, since you're trying lots of different mediums it's unlikely this alone is the problem, and i would still guess over-watering after pop to be the issue.
I'll wish you all the best with the next batch dude!