Windows versions beginning with XP SP2 limits opening TCP connection attempts to 10 at any given moment. If there are more concurrent TCP connection attempts, Windows generates a warning:
EventID 4226: TCP/IP has reached the security limit imposed on the number of concurrent TCP connect attempts.
Since XP SP2 there are only 10 concurrent TCP connection attempts possible. This does not limit the total number of connection attempts, just the amount that can be opened concurrently, previous versions of windows did not have this limit.
Event 4226 warnings from normal use of BitComet does not indicate a problem, and is to be expected.
(A connection attempt is a query to a computer, if it accepts the TCP connection or not. If the target computer does not accept the connection, it will wait a few seconds, until a timeout occurs and the connection attempt will be canceled.)
BitComet 0.55 and above has been modified so that it can work within this limit without any configuration changes.
With normal usage of BitComet, the target number of peers are obtained in less then a minute with or without the TCP limit in place, so it is only recommended that you install the patch only if you know exactly what you are doing, and have a specific reason for wanting to do so.
If you choose to apply that patch, you will be able to change the Max Simultaneous TCP connection attempts in the BitComet Options → Advanced → TCP/IP Limit.