Lately, I'm having some problems in Myetherwallet.
Sending a token always fails.
Either you don't have enough ETH on your address to cover fees or you using device with less RAM like mobile. If the latter is the case and you got enough ETH for transaction, try transaction on Desktop or Laptop and it will happen easily.
Losing tokens
Losing tokens

I don't think MyEther has any hand in that, it is simply an open-client and don't save any info with it. Always track your address on Etherscan and Ethplorer to see if tokens are present on address, you might confused yourself on MyETH as you hadn't loaded the full list of assets on it.
Token retrieval with no fee.
The most probable reason for it is that the token you trying to send is sill locked by the token owner. If a token is locked and you broadcast a transaction, miner will take the fees but won't complete the transaction as it is your fault.
What happened with Myetherwallet? is MEW no longer secure?
if Myetherwallet implementing 2FA might be safer.
If you really dislike using MyETH then you should possibly search for new client to conduct transactions. Best alternative is Idex.Market. Simply import private keys or Keystone File and start using it. Idex is much more simple than MyETH