Yes, you can always access your coins regardless of what happens to the app. Coinomi is a decentralized service and the keys for your funds are with you, not on our servers. On top of that, we're not planning to shut down Coinomi any time soon! As long as you have your recovery phrase, your funds are permanently safe no matter what happens to Coinomi or any other service.

The recovery phrase is the master key to all funds. By setting up the app with a phrase, you give it enough information to generate private keys to your coins and check their balances on the blockchain. By simply using the recovery phrase on a different wallet, you can access your funds via that wallet the same way. If the other wallet doesn't support recovery phrases, it should support individual private keys. You can follow the instructions here to access your private keys. To import a key into a coin's main desktop wallet, the common procedure is to open its console and type the command "importprivkey KEY" (replacing "KEY" for the private key of one of your addresses). Repeat for each address where you have funds.

Rarely we shut down servers of a specific coin, when it comes to planned delisting. In this case please read this article.