Wireless Router Extender disconnects after a few minutes

I have a D-Link DIR655 that sits next to my desktop in the basement. It communicates just fine with two laptops that are on the first floor-about 10-15 feet away-straight line distance. It also does just fine when I take the laptop to my screened in porch, which is about 35 feet away, thought the signal strength is pretty low.
I also have an iPad and an iPhone3Gs. They struggle, buffer, and lag a little when I sit in the porch.
I bought a refurbished Netgear router extender WN3000RP. Setting it up and connecting it was no problem. However, even though it's signal strength is excellent, it drops the connection to the web after just a few minutes. This is true on all 3 devices and regardless of their distance from the extender.
I've been in contact with Netgear and they have 3 or 4 tech guys who randomly pick up my progress reports and say they understand my problem. So far- no solution.
Thus far, I've changed channels on the router, disabled channel auto select, reset the extender, updated its firmware, and the latest suggestion is to change the security authentication on the extender only. I haven't done this yet, mainly because I'm not confident that it'll do anything.
The D-Link router is an n, and the extender is a g.
I have no problem staying connected via the router, except that I wanted better response time when I moved 35 feet away.

 

Thanks Tony. I tried to avoid drilling through floors and walls, but I agree-the extender will probably not work out, no matter what the Netgear support people come up with.