Updated 2020-04-29
It turns out to be an issue in TLS version of the windows desktop version. We've released a new version of Bither Desktop to resolve this. Head over to bither.net to download the latest version and it will be all fixed.
I'm the developer of Bither. Sorry for the late response.
No need to worry about your money and Bither is not a scam. Bitcoin.org has a restricted review process to list wallets on it. We can never get access to your private keys, thus your bitcoins are safe in Bither.
Bither is a decentralized SPV wallet. It needs to connect to other bitcoin nodes and sync block data to get all your transaction history. But in some network conditions it would be too hard to connect to any nodes. Bither relies on background processing to help you keep up with the blockchain tip. But mobile devices often have limit on background running time.
In your case, I think you are not syncing to the latest blockchain data. Though I'm not sure what caused this, but there is an easy way to fix it.
Update to the latest version, open Bither, swap to the right page, click Advanced Options -> Reload Transaction Data. This will download all your transaction history from 3rd party block explorers. And then you should be able to see your bitcoins. Like @Murch mentioned earlier, you can use Network Monitor to see if you are catching up with the blockchain tip and what's going on.
If you have any further questions, feel free to contact our support crew listed on the website. support@bither.net.