I had this problem also...it has happened to me twice. The game suddenly lags badly and everthing, including saving and loading takes 10-20 times as long. Even trying to ALT-TAB to desktop takes forever. It's just like the CPU usage has spiked to 100%, what with the input lag and everything. Someone mentioned that quick traveling to another location can sometimes resolve this, but it didn't work in my case.
I restored an earlier save and the problems persisted. How does loading times of 15 minutes strike you? 15 minutes! I honestly thought the system had crashed, but the slow flickering icon on the bottom right corner showed me that the game was still chugging along. And when the game finally displays, everyhthing was loaded in slow motion - i.e. your Inquisitor initially appears in an empty game world, and then the enviromental textures will appear, then the animations etc. And with the terrible lag, your're essentially playing a slide show.
The first time it happened I was fairly early in the game, about 10 hrs or so. I had fast travelled from The Hinterlands to Haven, and boom! The game ran like molasses from that point on. I remembered the message "lost connection to the Dragon Age servers" for some time before the game got really laggy. I stopped playing for a couple of days...loading times of 10-15 minutes were no fun 🙂 and the issue mysteriously resolved itself after a couple of days - even with the identical save game. Go figure.
The 2nd time happened last night - I was in Skyhold playing pranks with Sera, and bam! At the last cutscene, the game suddenly became super laggy. And what do you know? When I quit the game to the main menu (took about 10 minutes), the message "Lost connection to the Dragon Age servers" appeared! That's the common theme in my case.
I wonder if the flaky connections to the servers caused these issues. Shades of Simcity? And what the heck does it have to do with a single player game? Sigh