Hi Murphy,
I've got one of these left over from my old tank before I tore it down ready to restart a new scape (not sure of the exact species, it was from Java Plants, think it was a Tiger Lily or something like that, this was before I paid attention to plant names too much). It used to grow like a weed, it looked a little like yours when I first got it, I don't think they like being moved about and seem to sulk for a while before they start to grow.
It was in a low-tech tank (though partial neglect and partial lack of knowledge): monthly-ish water changes, 3x 20w T8's, heavily planted, a fair bit of accumulated mulm. As a result of the light, it reached for the surface and it's leaves became massive, but it did look really impressive but tended to take over, so I think it can survive without additional CO2 ok!
Every so often I used to prune it when it was getting silly (snipping the leaves off near the base) I'd take off about 4-5 tea-saucer to side-plate sized leaves! The guppy fry loved them though as it gave them a safe place to hide.
About that time I read that if you kept cutting the leaves off before they reached the surface it'd start to produce smaller leaves that would stay submerged for longer, so I started to get more vigorous with my pruning.
It split into 2 or 3 plants during that time. I took one of the smaller ones and put it into my little nano-cube when I set it up, thinking it'd provide a bit of colour until the other plants grew in, but under the brighter light (11w over 25l tank) it's not quite such an aggressive grower, it's growing happily submerged. It's leaves did become a bit algified but more recently (since deciding to rescape my main tank and joining this forum) I've begun a campaign of fertilising and adding Flourish Excel to the little cube to see it's effects and algae has almost gone and the leaves are pearling underneath.
The only thing I'd say is, yes they do have slow and fast growth periods (from my observations) and that I don't think they like to be buried too deeply in the substrate. currently the last 1cm of my lily's roots are all visible above the substrate, it might not like being too deep in the sand.
Also, older leaves, do tend to melt a bit rot down if they've had the slightest bit of damage, don't worry too much, just snip them off near the base, one problem I get is sucking them with the hose by accident when siphoning. So long as there are new leaves growing from the base you don't have to worry too much.
Probably best to give it a bit of time, and maybe sweep a bit of the sand off the roots? (based upon my limited experience)
Cheers,
Matt
Anyone else, please feel free to contradict if you know better