Sorry to hear that. Maybe try it again but let the wood dry out for a few weeks before wrapping it up. You can check for regrowth. Also maybe make a wider separation like 4 inches so it's more difficult to bridge.
Letting cut dry out is not necessary for lychee. This is more common practice for longan.. And even then the cut only needs to dry out for one day before applying moss.
More likely is the cut separation was not wide enough. Suggest making the cut 1.5 to 2 inches wide. Also make sure to very carefully remove cambium layer all the way around. Sometimes you don't see the bottom of cut, leave a little strip unscraped, and that will be enough for the cut to bridge and heal itself, and therefore will not root up.
Make sure to select a branch well exposed to sun. Branches in shade will not root up.
Using rooting hormone on the cut supposedly help the air layer to root up faster. Personally i never use it and still have high percentage root up, but maybe have to wait a bit longer for roots to form?