When the manage subscription link takes the user to the account login page even if they're already logged into their account, then this is usually because of a domain name setting. In this situation you'd need to use a different link then the one specified in the Recurring Orders app admin. The app admin will list something like this:
Note that the above example has .myshopify in it.
If you navigate to any other part of the store and the domain name doesn't show the .myshopify part (ex. www.myawesomestore.com), then you may need to copy that domain name and replace the domain name in the link that Recurring Orders gives to you. Here's an example:
Using this version of the domain name should take the user to the manage subscription section on the store front if they're logged into their account and press on the link.