Same thing happens with Japan - the only starting clipper ship of their navy soon gets reduced to 5% health. And indeed, the problem is all about naval bases and supplies. To be able to maintain a fleet, you need a naval base. And to get naval bases you need technology, which is available in a naval reform if you have not westernized. As for supplies, if you haven't westernized you either need to have someone producing some clippers, or somehow buy the clipper ships from the market (which is near impossible during early game).
China can maintain a decent navy though. They have enough artisans who can produce a sizeable amount of clippers for their navy. They have all the goods needed most of the time, and don't even need to westernize.