I understand that publishing will make it static. But the idea is there are a number of IPs in the 10.20.15 range (namly 129-191) that will need to be nat'd. I don't want to publish them all especially when they aren't all on or setup all the time. So I'm guessing that you are suggesting that I publish some other IP rather than the entire network.
Re: the modem comment; did you look at the network diagram I attached? The 172... is the inside interface of the modem. The outside is getting a public from the ISP. Sorry for the confusion.
While I don't disagree with you on the ping, I can assure you that I was able to duplicate the problem and fix. From this desktop (1.20.15.130), I would lose connection to the internet. My default gateway is the SRX ge-0/0/1.0 (10.20.15.254) and my default DNS is a vm running in my network (10.20.15.172). The DNS has a forwarder of the ISP's DNS address which is how I resolve outside addresses. The SRX has a default route of 0.0.0.0/0 to next-hop of 172.20.15.1 which is the inside address of the modem. When I lose connection on the .130 machine, simply pinging the 172.20.15.1 address restores internet connection - usually the first ping or two will time out. While connection was NOT working, verifying NAT and routing using the traceoptions looks exactly as it does when the connection IS working which is why I started thinking arp. Monitoring the ge-0/0/0.0 interface traffic would show constant ARP requests for 172.20.15.130 by no responses. If you have something else I could look at to troubleshoot, I'd appreciate it. But for now, I've just changed it to interface nat which seems to have fixed it.