If I were you I would switch towards Binance as soon as you can: low fees with their personal token, a lot of new cryptocurrencies are added there sooner than on Bittrex, overall more stable in my experience so far.
With this said, I still trade on Bittrex (I just love first blood) and they are not doing anything shady, you can trust your money are safe there, probably their network is just overwhelmed by the new investors excited by the altcoins rising this quick and for this reason they are having problems with withdrawals and deposits.