First you should research some of the standard terms and conditions in support contracts. For example 24/7 365 support could mean "we will arrive at your office within 4 hours of being called to begin working on the problem" which would be much different from "if the system goes down and we have not gotten it back up within 4 hours we will credit you $100 per hour for every hour over 4 until the system is restored to service" The former is basically "best efforts" while the latter is a performance guarantee. The former really doesn't really mean all that much because you could have someone on-site within 2 hours and then take 8 weeks to fix the problem, probably not what the customer wants. On the other hand you probably don't want the later simply because problems may occur which are beyond your (or the customer's) control, such as a bug in a third party software library that you used and which you would be dependent on the vendor to fix.
As you can see, these two options should be priced quite differently as the risk, and potential costs, to you are quite different. If priced appropriately, either might be a reasonable option. It really depends on the importance of the system to the client. For example suppose your application was a payroll system for a company with 10,000 employees and if they are late with payroll it could cost them lots of money as well as lots of disgruntled employees; they should be willing to pay big bucks to support that system. On the other hand if the system is an internal website for the annual company picnic...
You need to sit down with the client and determine the appropriate level of support, consequences of an outage, and an appropriate service level agreement to meet their needs and yours. Then work out a fair price.
