For the first problem, is it not possible that the user is entering a non-existing extension and Axon then transfers to that 'extension' and then the call is dropped? As a fix, you can specify a range of values that can be accepted, and if the user enters an incorrect extension they are asked to input the extension again.
As for the second question, I'm not exactly sure what causes dropped calls. I myself have only experienced them a couple-few times with VoIP and usually it could be explained by an interruption in the internet connection of some sort. I suppose it could also be caused by limited bandwidth (e.g. if several calls are competing on the same Internet connection, and that connection is not very high bandwidth, some calls could simply drop-out after not being able to successfully relay the SIP messages / audio to the server and back maybe?
Is the second line you have with the same company using the same voip server? e.g. if the host name is sip.voipserv.com, is the second line also sip.voipserv.com? If not, it could indicate that the new line is using a new updated server which could be using a newer version of the SIP protocol that perhaps NCH software does not fully support (perhaps?), if it is the same I cannot think of an explanation right now.