Update:

It looks like the solution carefully provided by stlpaul is absolutely correct. I have used the "--dpd-idle=0" additional suffix and now I am staying connected, hopefully indefinately. I have run a ping and have successfully pinged up to ping sequence 1,100+, which tells me the connection is solid.

In short, it seems my problem was over-reliance on a GUI VPN front end program for vpnc called vpngui, version 5.4.4. It seems the next step would be to somehow edit the vpnc-gui configuration to add the "--dpd-idle=0" additional suffix, which would complete this super setup. This may involve making changes to the source code for vpngui, version 5.4.4 to add the "--dpd-idle=0" additional suffix by default to every connection it makes.

I am very new to Linux, but I would not shy away from recompiling vpngui, version 5.4.4 to make this change. Can anyone offer any advice on how we could make this small change to vpngui, version 5.4.4?

Thank you very much