Can only get inbound RDC after first making outbound RDC

I am having problems using RDC to connect to an HP laptop running Windows 7 Ultimate, 32 bit edition. The HP laptop is connected wirelessly to my home router. The second computer is an iMac (running same OS as HP) cabled to a switch, which is cabled to my home router router. A third computer, a Thinkpad running Win7 64 bit Pro (and cabled to the same switch as the iMac), behaves identically to the iMac, so I won't mention it further.

I can always RDC from the HP into the iMac, but have problems RDCing from the iMac into the HP. I will get the error "Remote Desktop can't connect to the remote computer for one of these reasons: 1)Remote access to the server is not enabled 2)The remote computer is turned off 3)The remote computer is not available on the network"

When this error appears, I am unable to ping the HP from the iMac. I am always able to ping the iMac from the HP.

The HP is awake when in am trying to connect to it. In fact, both computers are set to never sleep or hibernate so I won't have to wake up a computer to RDC into it.

Both computers are set up to allow incoming RDC connections. I have confirmed that the antivirus and Windows firewall settings on the HP and iMac are identical. I have even tried disabling both Windows firewalls, to no effect.

Now here's where it gets strange. If I first RDC from the HP into the iMac and then disconnect, I can then ping the HP and RDC to it from the iMac. If I reboot the HP, the problem comes back.

It looks like there's something about initiating a connection from the HP that allows it to then receive inbound connections, but I just can't figure it out.

It's a minor annoyance, but any ideas would be appreciated.

I would check the firewall settings on the HP computer make sure you have an inbound rule to allow RDC or port 3389.

You also wont be able to ping the PC by default ICMP traffic is blocked.