Since both are slowing at the same time, it could very well be a network issue. Are all the computers wired directly to the switch? With AC Utilities, you can test the speed to and from the database. I would do a test right after a restart and then one when you think it has slowed down. Comparing those numbers will give us a good idea if it's the network or the computer. Similar times points to an issue with processing rather than connection. Significantly higher times indicate a network issue.
You can also check the RAM usage on the server. Open up the Task Manager to check the memory usage. If it's near 4GB, you can always add more. 4GB Sticks are $20. I suggest you do the same on the desktops.
The other possibility is that the main computer's hard drive is heavily fragmented. What makes me think that is when you said this "...what always works is if we run the AC utilities on the server." As time goes on, more and more "stuff" (scientific, I know) gets indexed (SQL and Windows Stuff). Since SQL express is limited to 1GB of RAM, it starts getting saved on the hard drive. Hard drives are slow and it will show as time goes on. That's why a lot of people see improvement when they restart their server/run AC utilities. Again, I suggest you do the same on the desktops. Auslogics Disk Defrag is quick defragmenter. Windows Defrag can take some time.
Gigabit switch isn't a bad investment. 10X times the speed of traditional 100 mbit connections. Especially with larger II, it's very useful. I would use these after you rule out the above.
D-Link:
http://www.amazon.com/gp/product/B0...TPFTA&linkCode=as2&tag=learnc-20Cisco SMB:
http://www.amazon.com/Cisco-SG100-1...3630160&sr=1-1&keywords=SG100-16