Is the machine actually burning oil? How do you know? How many pints or quarts per 1000 miles?
What color is the exhaust smoke? Black? Blue? Black smoke is caused by excessively rich fuel mixture. Blue smoke is burning oil.
Start by doing a proper engine oil and filter change with Honda specified oil not some magical snake oil, and a Honda oil filter. Record the odometer miles.
Then drive it normally for 100 miles, shut it off, let it cool, then check engine oil level. If down, how much? If it's not a significant loss continue driving to 200 miles or 500 miles. Determine exactly the amount of oil required to refill at a specific number of miles.
If, in fact, your engine is burning oil remove the spark plugs and perform a compression check. A compression check will determine if the engine or perhaps one or two cylinders have worn or damaged piston rings or valve guides.
That would be a fact that would determine if the machine will require an engine rebuild..