Hello, Openheaven.
I've been having the very same issue, viz., Apple's Mail app has suddenly begun to download new messages from my Gmail account very slowly — by which I mean that after clicking on the Mail icon in my Dock, the app opens (evidenced by the menubar), but the "Viewer Window" doesn't display for (sometimes) up to 15 or 20 seconds. When it does so, the messages populate the window almost instantly, as before, and all other features of the app continue to work normally (as before all this began). Quitting and immediately re-opening the Mail app yields the very same behavior, except that the delay appears to be a bit shorter than the day's initial opening.
Initially, I thought this may result of processing of Rules I had set up in Mail's Preferences, but disabling all of the Rules has had no perceptible effect on this problem. Nor does this improve if I disable all Junk Mail filtering. Moreover, if I were to log into my Gmail account via Safari, the Inbox messages continue to display almost instantly, whereas if I were to open the Mail app at this time (Safari still open to my Gmail page), it still takes anywhere from 10 - 20 seconds to display the information..
Prior to this strange and unwelcome behavior of Apple's Mail app, I hadn't made any changes to my Apple Mail Settings, nor to my Google Account's Mail Settings, nor to my router settings (Airport Extreme) or cable modem. Nor am I experiencing any other perceptible slowdown in Web traffic, including the sending and receiving of messages once Mail is open and running. This has been a vexing problem to try to resolve.