If you're having issues with one of your accounts in Liftoff! you might need to remove your account and log back in. On the add account page you can long press an existing account to remove it and log back in. But if your instance's website isn't logging you in reliably either, there may be something else going on or you might need to clear cookies for your Lemmy instance's website as well.
There was a security vulnerability exploited on multiple instances last night and a lot of instance admins invalidated all existing login tokens. I don't know if there's a Lemmy API response for invalid sessions, but if so, it appears we're not handling it in Liftoff. Regardless, I expect there to be changes to the Lemmy API relatively soon to address some shortcomings in the way login sessions are handled. When that happens, we'll try to handle invalidated sessions in a nicer way (i.e. with a banner saying you've been logged out potentially).