is one thing - it simply means the computer's wireless adapter has found the router - but connecting to the router depends on the individual machines being able to get an IP address.
Diagnosing network problems can be a frustrating business, but from what you say it seems to me that the problem might be associated with IP addresses. I'm going to assume that you know little or nothing about this, please forgive me if I'm wrong.
Each time a computer tries to connect to a router it needs to be assigned a unique IP address, so the router can identify that particular machine, and send data to it. The IP addressing is handled by the router's own DHCP server, and numbers are assigned on a lease basis - that means they expire after a predermined period. The lease period varies, depending on the router's configuration settings, and you can alter the lease periods to try to help resolve connection problems.
This may not be the cause of your connection difficulties but there's a chance that it is. Ask your IT advisers to extend the router's IP lease period. They'll do this by accessing the router's configuration settings, and if you feel up to it you could try it yourself; you should find instructions in the documentation that came with the router.