if you plan to keep the machine, for serviceability sake i would get an axle and hubs. i think the reason so many people had this problem is they did not crank on the axle nut hard enough. if you do buy the parts tighten it down till its snug and observe the castle nut and cotter pin hole in axle. i always aim to crank it 2 notches farther on the castle nut. when i tighten them i use a 2 foot breaker bar and have to sit on the tire to crank down on it.
the welding thing was fine on the farm, when miles from a honda dealer and before the days of ebay and craigslist. the parts are easy to find and will make life easy the next time it has to come apart.
Trikes: All Honda: 84 250r, 85 86 and 87 250sx, 84 and 85 125m, 79 82 84 and 85 110's, 73 us 90 and 77 atc90, 75 atc70
Cycles: Honda: 71 cb100, 78 cb750 coming soon cb750 trike. Yamaha: 67 yds 3 (250cc, 2cyl, 2 stroke), 82 750 SECA
Other toys: Chenoweth VW sandrail dune buggy, old race go kart, racing mower, 76 Arctic Cat Pantera 440 snowmobile
KEEP IT ON ALL 3 OR AT LEAST 2 AT A TIME