IMO the main two reasons people leave shards other than Atlantic (SOTA) are economy and lack of people to play with.
I think lack of people to play with is a lesser of the two problems. Many denizens of SOTAs like the fact that it's easier to hunt when there are no crowds around. And while there are fewer people, the communities are often tighter. You won't find a group every time you play, but you will get it often enough, and will appreciate companionship that much more.
Economy (lack of) though is the big killer of SOTAs. And economy is dead not so much due to low pop, but because of Shard shields and weekly vendor fees. Shard shields make a giant sucking sound [(c)Ross Perot] while removing everything of value from the shard. Weekly vendor fees make selling anything a losing (in a literal financial sense) proposition. When it takes 2 months or longer for a fairly priced item to sell, there is no way to price it so that it would make sense to both the buyer and the seller. This disproportionately affects returning and new players because they are less likely to have shard shields or have friends with shard shields. Thus, you have these players who are unable to sell their loot, or buy what they need. Some of them move to Atlantic. Many of them leave UO.
How to fix this? There are a couple of ideas that have been suggested:
1. Taking away shard shields will alienate many existing players - not a good solution.
2. Making everything shard bound. I am afraid that horse has left the stable. On many SOTAs the population is low enough that you need access to a bigger market in order to be able to buy some of the rare items. A specific mastery III might take years to farm, and the times when this was acceptable are long gone. So I think stopping cross shard trading at this stage would make things worse, not better.
3. What I think would help quite a bit:
a. Switch weekly vendor fees to a point of sale fees. Make them reasonable, otherwise you will keep commerce just as dead as it is now. Inflation is a far lesser evil here, so if you need gold sinks, make them elsewhere. If you are concerned about people using vendors for storage, look at any other MMO that has figured out this problem. Oh, and auction safes without search function are not a solution. People don't want to spend their precious game time manually sifting through the offerings.
b. Make cross shard trading open to every paying customer. Ideally, make a central trading hub/AH. A less developer-demanding solution is to give everyone monthly shopping passes to the shard of their choice. Whatever income will be lost on transfer tokens will be more than made up on the subs that are not lost.