Do you, or should you, only rely on the computer for your pressure gauge or should you have a pressure gauge as a back up or are the computers that accurate?
When I first read the question, I immediately thought of wireless air integration, but also realize that you may be referring to 'hosed' air integration. The responses might be different according to which configuration you are asking about.
There are different schools of thought on the question of gas pressure redundancy, and air integration, and wireless air integration, and more than a few SB threads on the subject, which might give you a broader perspective (e.g.
http://www.scubaboard.com/forums/co...22654-gas-pressure-indication-redundancy.html), so a search using terms as simple as 'SPG AI failure' will yield a lot of information. There are some on SB who say that they see more failures with SPGs than with wireless AI computers / transmitters. That hasn't been my experience but I can't challenge theirs.
I am one who dives with both (SPG and wireless air integration), much of the time. I dive with a SPG ALL of the time (so, that is my 'gold standard'). When I use my singles reg with a transmitter, or remember to switch the transmitter to my BM doubles reg set, I also dive with a transmitter and AI computer, for the convenience. I have never used a 'hosed' air-integrated computer, but would view one as equivalent to a 'brass and glass' SPG, and would not feel the need for a back-up (unless I was solo diving).
For most recreational diving, it really doesn't matter.
If you are diving with only one or the other, you should be monitoring your SPG or computer (with wireless integration) with regularity and if it stops functioning, you generally thumb the dive. Of course, ideally, if you plan your dive appropriately, and stick to the plan, and know what your air consumption is, a gas pressure measurement device is only a back-up anyway, and you should have a good sense of when to turn the dive based on time and depth as outined in your dive plan. But, while I accept that as an ideal state, it is not the reality in most recreational diving.
If you are diving with both, and one fails, you continue.