I have read about a similar situation before on this forum before particularly Metamask was also the wallet that was affected. If the wallet is usually drained once you make a transfer into it, then it is a case of Sweeper bot which is like a script assigned to your wallet and this code automatically transfers the coins on a certain blockchain that is affected, in this case it could be the BNB blockchain.
MetaMask has recently provided a guide on how to
Fighting back against sweeper bots, read through it maybe it could help solve your problem