Sorry, I misread your post. You're talking about explorer not internet explorer, although if you apply the same method to the Explorer window, it will work in the same way. philwane's solution sounds quicker, and the explorer window will always be maximised.
I assume you have tried philwane's suggestion also, and that didn't work.
Try this. Open Windows Explorer. Drag the borders to the desired size. Hold down the Ctrl key, while at the same time, click File, Close. Then release the Ctrl key. Open Windows Explorer again to see if it works.
If not, do the same thing, but this time try the Shift key instead of the Ctrl key.
On the left hand side, navigate to HKEY Current User \Software \Microsoft \Internet Explorer \Main
Highlight "Main". From the menu at the top, click Registry (or File) and select Export registry file. You'll be prompted to save it. Give it a name and save it to a location you can remember. This is to back up your registry key.
After backing up, look at the right hand side, with "Main" still highlighted.
There should be an item under the Name column called "Window Placement". Right click it and select delete. Then exit regedit.
Restart computer, then open IE and resize your primary and secondary windows by dragging the borders and not by using the maximise button at the top right. Close IE. Restart IE to see if it makes any difference.
If not, go back to regedit. Go to HKEY Current User\ Software\ Microsoft\ Internet Explorer \Document Windows
Highlight "Document Windows" and export registry file as before.
Then look at the right and make sure that the data values are
height 00 00 00 00 width 00 00 00 80 x 00 00 00 80 y 00 00 00 00
Then double click the item "Maximized". Change the value data to yes. click OK. Exit regedit. Restart computer. Open IE to see if it works.