You may be surprised to learn that currently more than 20,000 amateur-built or experimental aircraft are licensed in the United States. And thousands more are parked in garages and hangars waiting for additional work.
One of the greatest benefits of building your own airplane within the experimental classification is that the FAA says, in essence, "If you can build it you can fix it." In fact, that's a major reason why budget-conscious flyers decide to build their own plane from a plan or a kit. They can do their own annual inspections (called condition inspections) as well as ongoing maintenance and periodic repairs. It's up to the plane's owner to make sure it's airworthy.
Of course, that puts additional responsibility on the owner to make sure all inspections, maintenance, repairs, and modifications solve problems rather than create new ones. However, people who invest hundreds or even thousands of hours into building something know much more about their aircraft than those who buy and hire planes, and they care about keeping their craft up and running.
Fortunately, most experimental aircraft plan publishers and kit manufacturers are conscientious about informing their customers about the technical aspects of their planes. In addition, many manufacturers encourage and assist user groups who help each other in the construction, flying, maintenance, and repair of their craft.
Can you buy someone else's experimental aircraft and maintain it yourself? Technically, yes. However, remember that it's totally up to you to not only make sure it's airworthy, but also to know just about everything there is to know about the craft. If you did not build it, you cannot perform the annual condition inspection — only the original builder or an A&P mechanic can inspect it. Review the builder's logs and records to make sure you know what you're getting into.
Again, I stress that if you are considering building your own aircraft — or buying one from the builder — contact the plan publisher or kit manufacturer (if still in business) and learn as much as you can about the plane you'll be flying. Also, join the EAA (Experimental Aircraft Association) and any clubs specific to your craft so you can keep informed. You'll find many resources for parts, services, technical assistance, and knowledgeable sympathy. You'll need all of them if you accept the challenge of flying and maintaining experimental aircraft.