If kept outside, Chinese elms are deciduous and will drop their leaves in the Fall. Even in southern California, my Chinese elms will drop their leaves - if just for two months.
Kept indoors, Chinese elms are usually treated as tropicals, and will typically keep their leaves throughout the year. However you have to provide them with bright light. I am not aware that you can provide an indoor elm with TOO MUCH light - heck they live outside here in SoCal in full sun - but you can certainly give them too little. Too little light and you start to see weak, leggy growth.
It is never a good sign if your tree pushes new growth that dies back, and then it pushes a 2nd round of new growth (weaker than the first) that also dies back. There are many possible causes... but looking at your tree I immediately wonder if the roots are dying / dead. If you let the soil dry out, but catch it in the nick of time, many of the roots will die, and the tree foliage will start to die back because the tree no longer has enough roots to sustain its foliage mass. Almost the exact same thing can happen if you keep the soil TOO wet and the roots die from being in a swamp. Often once a tree goes through this initial shock, it is tough to bring it back because it is in such a weakened condition. If it is a question of forgetting to water it, you simply have to start up your watering cycle and hope for the best. If the soil is swampy, you HAVE to address soil drainage or your tree is going to die. And while you are doing all of this, you have to give the tree enough light because light = food and energy.
If you need to soak your tree in a pot of water in order to get water to penetrate throughout the root ball, you have to repot the tree. If your soil is so compact/bad that water can't penetrate, soaking your tree in a pool of water is just going to kill it. Your tree needs to be in a good soil mix with good drainage. When you water your tree (from above) the water should instantly soak in and then drain out the bottom of the pot, leaving wet (but not saturated like a sponge) soil behind.