The short answer: if you own the source code, control the hosting and domain accounts, and have documentation, another developer can take over. If you don't, you may be locked out of a system your business depends on. The time to check is now, while the relationship is working.
An agency closes, a freelancer moves on, a relationship breaks down. The businesses that recover quickly are the ones that protected themselves in advance.
Your contract should state that source code and intellectual property transfer to you. Without that, you may have paid for something you're only licensed to use.
Ownership on paper isn't enough. You should have access to the code repository or an up-to-date copy.
Domain registration, hosting, DNS, email and third-party services should be in your business's name, with your own login — not only the developer's.
How the system is set up, how it's deployed, what it depends on, and where credentials are stored.
Common frameworks and platforms make it far easier to find someone to take over.
A good developer won't object to any of this. If one does, that's useful information.
At ZACODERS, source code and IP transfer to the client on delivery, on every project. We build on widely used technology and document our work so another developer could maintain it. We'd rather keep clients because the work is good than because they can't leave.