That may be true, but my router is a Cisco E3000, which is supposed to be a top-line router.
I have read good things about it.
If it can't handle the job, I'm reluctant to spend more time and money looking for another.
This isn't a hard job, any router that does NAT translation should be blocking this...100% of the time.
If your hypothesis about it being due to a response to an outbound connection is right, that only reinforces the importance of a software firewall that does controls outbound traffic.
To some extent, but looking at it another way...you might also want to evaluate the types of software that you install and use on your on your computer. If it's something like malware well then you obviously didn't put it there on purpose. But I don't know if I've seen much malware that opens up outbound connections to then allow port scans. Best case scenario they get a port listing of open ports, but are then blocked when they try to establish an inbound connection to those ports. I just don't see what the gain would be.
If this were me, I would do the following
1). Look at outbound logs on router? See if you are making outbound connections to same IP addresses that are getting flagged as doing the port scans.
2). Since this is a wireless router, be sure you don't have somebody leaching off your connection? Turn of ESSID broadcast, shut off DHCP functionality, use obscure network range in private range, enable MAC address filtering, use something like WPA2 with a horribly long security key.
3). Double check that your PC isn't sitting in a designated DMZ port. (I've seen this countless times)
4). Double check that you don't have a range of ports being forwarded by your router somehow. (less likely than above)
5). Call Cisco/Linksys and see if they have any known firmware issues, or bugs, or obscure configuration settings which could allow this problem.
Without a doubt, your situation would have me very concerned. But I wouldn't necessarily turn to a software firewall on my PC as my first line of defense to prevent it from happening....I'd rather figure out why the first line of defense products are not working.
I'm checking out at this point for the night, as it's 4:22am where I am and my kids will be up in about 4 hours.