There appears to be Windows 7 updates for all three versions of the realtek RTL8187 chipset. I suggest you try out the download in the link below. You will need to choose your version B,L or SE. Scroll to near the bottom of the page and click on the "software" link then scroll down again to find the Windows 7 download link.
If you are still having problems after the upgrade we can take a look at your router and see if it needs a firmware update. Realtek