Probably the normal behavior of the algorithm estimating the lfcSE.

Consider the simple case of a Binomial random variable. That's a coin-toss with probability p of a Heads. We know the expected count of heads after n flips is n times p, and the variability around that result is n times p times (1-p). My point is the variability is a simple function of the parameters p and n. Probably DESeq is doing something similar in your experimental setup, where the lfc-SE is derived from the data modeling it's doing. The variability modeling steps in DESeq will use the whole dataset and share information about the dispersion seen in each transcript, so you should expect some kind of relationship. Probably in a more controlled experiment you'd see a less clear relationship, but now it's doing what it can on limited information.

Since timepoint 1 has strictly lower SEs, it looks like that's the condition you have more replicates of. If you need to know how the numbers are determined, the source-code is available to look into. I wouldn't worry about it.

Edit: Worth looking into my own data for the same phenomenon. When comparing two samples in three groups (six total samples) my lfcSE plot is on the diagonal red line. No crazy loop, but the very coherent correlation is present. I'll stand by my claim that whatever makes one gene have high SE in one comparison also influences it in the other comparison, particularly since we're using the same third comparison group (your timepoint zero). I'll look into another experiment with more than 2v2 samples to see if the loop structure comes out at all.

Edit2: Here's the results on two experiments. The top row is two samples, symmetric Ax2 vs Bx2 and Ax2 vs Cx2. The bottom row is a varied dataset, Ax20 vs Bx6 and Bx6 vs Cx14. You'll see the correlation is a little more fuzzy but still strongly determined by the gene itself. Of note my SE are almost 10 times as high as yours. Could you post some code so we can see what analysis exactly was performed?