) Knowledge of client applications. To fix something in a timely manner, you need to know the application/architecture. If the client does not have documentation (or, as is more likely, they have outdated documentation), learning the architecture could mean a large upfront time investment.
) Bursty nature of support requests. This could be mitigated by doing consultancy/project work in the same market.
Particularly in early startups, the infrastructure tends to grow organically. Having an outsider help document the infrastructure and processes could be quite useful.
If anyone wants to discuss this idea more, my email is in my profile. I think there is a market out there for such a service - I'd love to hear from anyone who thinks it might be useful to them.
A per-server setup fee and a fee on any sys changes is reasonable, as is having the onus on the user to work with the sys admin service to test failovers etc. You could provide add-on services, like scaling advice and implementation etc. Since a lot of sys-admin is doing nothing (thanks to so brilliantly setting things up in the first place, right!) that time is billable to clients for services. That covers your second problem.
This is the kind of idea I'll feel sad about for not having a crack at myself, but I'd be happy to see it out in the wild.
--Supplemental--
Before anyone accuses me of being cheap, I'd be happy to pay $100 per hour, assuming the 'call out' would most likely be short in duration since it would be part of the deal that I supply a detailed wiki of the software under support.
The answer is: You have to find, and more importantly, be passionate about those problems on your own. If you aren't passionate, your execution is doomed.
1) come up with a business idea 2) build a site for me 3) market it for me 4) profit!
In that order.
Ok, seriously: 1) I need a CRM for influencers. Bloggers, journalists, etc. 2) I need Github backup service - weekly or daily. 3) Proxies as a service (sort of like TOR but with a friendly API)
Something similar to this is on my list of potential ideas, but I am not sure enough people would use it.