I have thought about doing something like this - providing a sysadmin service to companies who don't necessarily need a full-time sysadmin, but do need e.g. emergency response to system failures. I see two main challenges to making this profitable:

) 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 If the client does not have documentation (or, as is more likely, they have outdated documentation), learning the architecture could mean a large upfront time investment.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.