I don't think your trellis will ever stay tight unless the poles are sunk into cement, or otherwise supported; for instance, I have a long (30') bean trellis that is supported by big metal "U-posts", which are pounded into the ground and also bolted to railroad ties that border the garden. And we had a similar problem with the sagging with our "grape arbor" (we have 6 grape plants, just started a couple of years ago, supported on wires stretched between 4x4 posts). There are 2 rows, with a post at each end 20' apart, with 3 wires strung in between (also with turnbuckles). After this past winter they were sagging dreadfully, and my husband has recently dug down around each pole and poured in a good amount of cement for support -- hopefully that will solve our problem; there certainly will be he** to pay if we ever have to remove those posts!!
What might work for your tomato trellis is to use more poles (or boards) horizontally in between the posts, so that the trellis is more rigid. Hope this helps!
