i recognize this pic...

what responses did you get last time/???

is there any new info to share ..

did the plant not grow at all in the week or two.. since last time???

ken

I actually used spinach as my FFA project back as a kid. Spinach loves sand/silica, and not as wet as you seem to have it. I'd first move that top-dressing/mulch back from the plants, they look too wet. What is your soil medium? If it's too rich, it just might be the culprit, they love a very fast draining sand with a bit of soil mix. If you can get them past the toddler stage, leaf miners will really not do enough damage to kill the yummy leaves you are looking to eat.
Leaf miners leave thin white lines all over the plant, that look like worm-trails, Picture could show this, but too far away for me to tell. But they love young plants/cotyledon leafing, so you may be right.
Honestly, those plants are so young, I'd trash them, start over with new seeds, dry the soil mix out first to kill any fungus, then amend soil with lots of clean sand. Plant new seeds in new mixture. Mulch away from the plant after it is 4 or 5 inches tall, if you must (we never mulched spinach), don't let it touch the plants. Water them sparingly, deeply, not as often... you look to be over-loving them with water. :)
I'm not saying walk away from water, just cut it down, it invites fungus and all sorts of insect pests when environment is too wet. Azomite is great for spinach as soil additive, keyword it :)
Good luck New Gardener
PS: One last remark, this is really the wrong time of year to be starting spinach in Fl. Next time, start it in late November to early December, spinach hates the heat we are just about to endure.
Read the packet carefully, make sure to pick a type that is able to take the heat, you may even be able to start it earlier this Fall than I mentioned.

This post was edited by MsMorningSong on Sun, Jun 8, 14 at 20:46