I think you'll find that GPS is probably the best nav system with regards to warning the pilot when there is no GPS signal!...you get flags, messages, etc...Is yours a certified installation or is it a hand held mounted on the windscreen?
I've had spurious issues with a GNS430W ranging from signal degradation to complete loss of signal for some time without a clear pattern. It was eventually traced down to a defective unit. Note that in my IFR certified installation, the loss of signal did not make the CDI show an off flag!
The user interface of the GNS430W is absolutely terrible and its habit to constantly pop up stupid and irrelevant messages that you only see when you press a button trains pilots to not assign any importance to them.
I got my license when GPS was already ubiquitous and always considered the whole VOR/DME stuff to be rather annoying but after my experience with the GNS430W, I see myself tuning VOR/DME stations enroute and perform cross check.