Time Capsule (A1409, 1TB)
What is the actual model number on the base.. something here is wrong.. the A1409 never came with 1TB.. so it is either 2TB or the number is wrong.
Is the TC the main router of the network or is there a router in front of it and the TC is bridged??
It might or might not be relevant.. but helps to start from the right place.
What you are experiencing is not unknown.. Certainly Android OS which I presume some variant of is used by the chromebook is well known to have wireless issues with some routers.. it is because wireless is still at the voodoo stage of technology.
Here is a list of things I would do.
1. Make all names on the TC short, no spaces and pure alphanumeric.
Set different names for the two bands.. eg TC24ghz and TC5ghz. So you can try and isolate the problem.
2. Test now with no security on the wireless at all.. to see if this is a security issue.. this is just a test of a few minutes.. see how it goes.
Does the problem go away??
3. If it does work then use WPA2 Personal security with a purely alphanumeric password.. mixed case and numbers..
Does that bring the problem back?
4. If the test fails and the TC still falls over when the chromebook joins.. then I am afraid there is some issues.. and likely not going to be fixable.
You can test the chromebook with a static IP.. use something in the correct range and with gateway and DNS set like it is via dhcp.. just don't use an identical IP to anything else on the network.. again we are trying to find is the problem fundamental to the driver or is it dhcp server/client issue.
5. You have upgraded the OS and drivers on the chromebook to the latest available.
If you have done all the above and still have issues.. there is no fix.. at least not on the TC or on the Chromebook that will help.
The best way around the problem is simply buy a cheap wireless router as AP.. eg bottom end TP-Link N lite.. maybe $35-60. Set it up plugged into the TC and use that for chromebook connections.. this will generally work.. and is the cheapest way around the problem.