FPS drops after 2 hours of playing

You can try updating your graphics drivers. It is possible that your graphics card is having issues processing textures. I don't use AMD cards myself, so I'm not familiar with issues for those cards. Also some areas of the game are bad on FPS no matter what. Redcliffe is really bad for this.

But often this kind of thing happens when a program is running with a resource leak. This means some program is using up resources on the computer but not releasing them when it is done with them, so it just keeps eating up resources.

You should try closing any unneeded programs running in the background, especially any web browsers. You can also open your task manager (right click on the task bar and select "start task manager"). Choose the processes tab, and look for programs that are using up CPU power and have large memory usage. If you know what they are are they don't need to be running, you can close the process.

You should also try to understand what programs are related to these processes. Some are programs that load into memory at startup and do not need to be there (like Adobe autoupdater). But the reason you should know what should be running is so you can tell what is out of place. You might see a program called something like FQK23T8.exe  This nonsense programs are a good indication of a virus or malware that is eating up resources.

To see what programs are loading at startup, in windows 7 you can type "msconfig" into the start menu box that says "Search programs and files" and hit enter. For older versions of windows open up the "Run" command in the start menu and type msconfig.You can also open the command prompt and type msconfig. Once it is open select the startup tab and you can uncheck any box that you do not want to run at startup. Just make sure you understand what they are related to as some of those programs need to run, so only uncheck them if you are sure.

Memory leak is the likely culprit like was already posted.  One program that can help you do many things, one of which is to tell you how much memory is being used by a program is        https://technet.microsoft.com/en-us/sysinternals/bb896653.aspx   

It will tell you how much cpu, and memory different processes are using, allowing you to monitor if DAI is building up memory use when it shouldn't. 

The above process explorer will also tell you if something else is starting to run at that time and is taking cpu time away from the game.

Another issue that MAY be happening(not near as likely) is heat buildup.  You may have a slow build of heat in gpu/cpu that can be shed once the game is shut down, and doesn't build up enough to cause issue until you play long term again.  Again this isn't likely, because most likely it would happen quicker the second time due to all the related components being hotter already.  But a program like speedfan is good to have around anyway, and is handy for this situation.

If you have dual monitor screens, then having both of these programs up and running while playing would make monitoring both for the issue easy.