Read comment up-stream. I disagree with this standpoint and I'm sure can find you stories out there beyond mine to back up what I'm suggesting. DNS hosting as well is so inexpensive unless you're in the hundreds of millions of queries that really I see no reason to not look to hosted DNS solutions first. Even one of the premier DNS providers out there is only like $29 for a small-business plan.
Essentially, unless your website is not revenue generating (or is below the cost to make this feasible), you really should look at moving from self-hosted DNS.
There's about 10% of the internet that's using "parent centric" DNS resolvers. What that means is that when it comes to what name-servers to query for a zone; those resolvers pay more attention to what's in the parent-zone than what the child-zone lists for itself.
For that 10% of the internet; the TTL on the NS record set is out of your control - it's whatever the parent domain's policy is. Although you may have set a TTL of an hour - for nimble re-delegations on your end, you'll have to wait out the time-to-update from your registrar (usually an hour, but sometimes a business day or more, depending on the TLD) and then also update the TTL on their end. For most domains, like com and net, it's two days.
So if you need to add name-servers after a problem starts, expect it to take two+ days to fully roll out to all users.
That said, the progress follows a distribution, and you'll remediate things for many users quite sooner - but still probably not within an an availability target of even three nines per month.
