Branch Office setup

Question

Hello All.
I have a problem with a branch office setup, and I can't for the life of me think of what the problem is.
I have a remote office setup, using an ASA 5505 that is set up to establish an easy vpn connection to the central network.  The connection at the branch office is a 20/5 cable modem, the central network has a 25/25 fiber connection.
The issue I have is this.  Wired clients work fine at this branch office, at least 95% of the time.  I have a lightweight AP there that can come up and join the controllers at the central network, no problem.  I haven't done anything with H-REAP because there are really no resources locally they need that would allow them to do their work, so all traffic is tunneled back to the WLC.
Wireless clients can authenticate to the AP, and I can get 15-20ms ping responses from them all day.  Latency never comes close to the 600ms proposed limit with CAPWAP.  Yet, for some reason the performance of the clients is problematic.  Webpages will frequently not load correctly, they experience some freezing, and with one application we use - it refuses to load completely.
If we bring these same computers to an AP connected to our central network, on the same SSID, they work flawlessly.
Something about this particular location is causing a lot of grief for our users.
For what it's worth, we are running WCS 7.0.230.0 and the WLCs are on 7.0.116.0.  The ASA is running a pretty basic configuration, pretty much out of the box with the easy vpn configuration entered.
Any help on this would be appreciated, I am at my wit's end with this setup.

Answer 1

Yes, 20/5 Download/Upload. 
So I did as you suggested, here are the results with a 1400 byte packet:
Ping statistics for 172.16.253.50:
    Packets: Sent = 100, Received = 99, Lost = 1 (1% loss),
Approximate round trip times in milli-seconds:
    Minimum = 17ms, Maximum = 2208ms, Average = 42ms
That 2208ms response was an anomaly.  I ran it again and got this:
Ping statistics for 172.16.253.50:
    Packets: Sent = 100, Received = 100, Lost = 0 (0% loss),
Approximate round trip times in milli-seconds:
    Minimum = 16ms, Maximum = 93ms, Average = 21ms
With this one specific application we're testing with - it stops loading at a predictable point, every time.  However, I can remain VNC'd to this machine the entire time, and do anything else on the machine, but the application will fail to load at the same point every time.  But like I said, if I bring that client back to our main network, it works just fine, so it's not the application itself causing the problem, and we have other, smaller issues with other applications we have.  It's really bizarre.
It's really not acting like interference.  I just set up a new site with an identical configuration - but with a 3502i AP, and I can replicate the behavior at that location too.  Unfortunately at this time we don't have anything to study the traffic with - I actually have a call on a solution for that this afternoon.