From the client's POV, it seems to make sense - they pay for say, 20 hours a month, so they want to see 20 hours per month being performed. In your opinion, what is the average time you actually put in compared to what they are paying for? Is your rate discounted as part of the plan? It may be that the client is simply wanting to renegotiate the fee to make them feel better about the unused hours (again, similar to why people want to renegotiate a phone plan).
And what are these improvements they are looking for? That sounds very open ended and all-encompassing, and I suspect after a couple of months you'll be finding it hard to discover these so-called improvements, and it could turn into a bit of a nightmare for you. And what happens if you deem there to be no improvements to be made - what happens then to any unused hours?
I feel 'improvements' would be better handled as a single project - i.e. assess all improvements required, quote and perform the work. Maybe with an annual re-assessment.
From your POV, the idea of a maintenance contract is most likely the simplicity for you; there's no hassle with billing, its a guaranteed monthly income, and the onus is on the client to find you work to do. What they are suggesting take a lot of that simplicity away from you. It's also worth remembering that a maintenance contract guarantees your client x hours of your time each month - they should not forget the value of this, compared to the common situation they'd experience without such a contract - 'Oh, we're pretty busy, it may take a few weeks to get that done for you'.
If it were me, I'd suggest handling improvements as a single project and perhaps renegotiate the terms of the existing deal - e.g. if in the previous year they used 15 hours a month on average, change the contract to a 15 hour one instead. Reduce the hourly rate a little for those 15 hours (but remember the benefits to the client in having the contract, so don't go overboard with the discount) and any time over the 15 hours is billed at the standard rate. Of course, also point out that any time over the 15 hours is not guaranteed to be completed as quickly, so reinforce the benefits of them 'securing your services' for more hours a month, just in case.
Basically, work out a good deal for them, but one that you feel is sustainable and profitable for you as well.