Richard Oedel replies: Old lathes mostly use ball or roller bearings for the headstock, and as such, if well designed and lubricated, will last for a long, long time with no reduction in accuracy.
If you have an old lathe with a sleeve bearing (look up these terms in Wikipedia if you aren’t sure of them), it will gradually get worse and worse. I don’t like sleeve bearings for lathes, which is why most good quality lathes since 1910 have ball or roller bearings.
Roller bearings take more load. Ball and roller bearings mostly fail by “brinelling” which is basically small dents in the bearing, usually caused by an impact to the bearing (hitting the headstock with a hammer to loosen it is a good way to do this) and there is no cure but to replace the bearing(s). This failure mode usually announces itself by a gradually increasing rumble or whine in the bearing area, but sometimes just by a louder and louder lathe! And the bearing gets hot. If you don’t lubricate the bearing, it will fail.
Some are lubricated for life (the life of the bearing, not your life) and sealed. Others are designed to be lubricated from outside using oil cups or grease fittings. Use the recommended lubrication from the lathe maker. Not too much (it goes everywhere) and not too little (it gets hotter and whines—see above).
If you have to replace the bearings—let a pro do it. The chances are pretty high that you will damage the lathe and new bearings in the process of removing and re-installing them. Ask a local machinery dealer for a recommendation. If the person can change the bearings in a multiple horsepower motor, the person can change the bearings in a lathe.
Jon Siegel replies: The bearings of the headstock are designed to hold work commensurate with the size and weight of the lathe. Heavy chucks are probably not a factor, but the weight and balance of the workpiece could be. Spindle speed is also a factor, and I think turning light work at very high speed is probably more wearing to the bearings than turning a large bowl blank at low speed. It’s impossible to say how heavy a workpiece your lathe will handle because there are so many variations of headstock and bearing designs. Usually the limit on workpiece size is not the bearings, but the stability of the lathe bed and tool rest.