Do you live in a location where lilacs are common? They require quite a bit of winter chilling in order to bloom.

Other than that, I'd strongly suggest that you stop moving the poor thing so that it can establish itself happily into a permanent location.

Next season's flower buds, if they form at all, develop very soon after the spring blooming period. No pruning should be done after that time, whether you see buds or not.

Depending on how far south you are in the South, you'll find more problems with getting flower formation as rhizo_1 mentioned.

Prune the lilac ONLY immediately after they flower (or in your case the time of year they should flower) which would be in April in the South. Don't prune now, since the flower buds are being formed in the summer (you'll see them become plumper and plumper at step tips).

Hopefully this last location you relocated the lilac to is in the coldest microclimate you have, such as being exposed to cold winter (NW) winds and NOT protected or warmed by nearby building foundations or pavement.

Truly the "soundest" lilacs for warm Southern gardens is cutleaf lilac (Syringa laciniata) or Manchurian lilac (Syringa patula), which is usually seen sold in the cultivar form of 'Miss Kim'. Note these really only do well as far south as zone 8.

Here is a link that might be useful: Cutleaf lilac info

There are always exceptions, but these two lilac (cutleaf and Machurian) species get more problematic for flowering when you get in zone 8b.

Here's info more on 'Miss Kim' that I couldn't add in the one links box in the last posting.

Here is a link that might be useful: Miss Kim Machurian lilac info