You may be getting "prompted" for a couple of things. First, to enter your credentials to login. If you clear you cookies you will get prompted for your username and password. This will happen with OAuth 1 or 2. But to answer your question, we don't support auto-approvals for OAuth1 authorizations. You should hold on to your access token and should not have to re-prompt the user for continued API access.
This is where I add the standard disclaimer that if you should strongly consider using OAuth2 instead of OAuth1. We've deprecated OAuth1. OAuth 2 is easier to code and the user experience is much improved.