Calfskin heads do dry out over time, become brittle and can tear. As CT Pro has said, they don't last forever. However, being rawhide, they are quite tough and will last a long time with care. They , like anything else were also made well or poorly. Many of the older heads on American drums were made by Chicago Rawhide and branded for the individual companies. There were different quality heads , based on the degree of imperfections and the evenness of the thickness, so just because a head is calfskin, it isn't necessarily good calfskin.
Here are the standards I have gone by, over the 50 or so years, I have made and used them.
Soften and clean them with with cold water only. They do have a small amount of natural fat in them and any solvent, even soap will dissolve and remove some of those fats. If an old head is brittle, it can be restored to a more supple condition with the addition of some fat. Neatsfoot oil,which tends to oxidize leather, is derived from the legs of cattle, which due to their potential of exposure to extreme cold are blessed with a lighter, oilier fat than the body does. The fat associated with the skin, is more lardy, so the best fat to replenish the head is beef tallow. Lard is easier to find and a suitable substitute. Both, are easy to render at home , from purchased beef fat or pig fat and will keep in a jar for sometime, with refrigeration, extending the shelf life . Light oils will reduce the strength of the head, if overused.
I have stitched heads but it is tricky. Usually the head tears, due to shrinkage and the two edges are too far apart, to draw them close without the stitches pulling through their holes. An option is to stitch the tear, without pulling too much and therefore reducing the threat of further tearing, then gluing a calf patch over the tear. Cyanoacrylate( crazy glue), has worked well, probably due to it's surgical apllications and affinity for skin, despite it's supposed low shear strength. A thinned hide glue also works but causes a bit of browning. I'm sure there are other cements that I haven't tried that would work too.
A special mention has to be made about slunk or more properly, slink heads. These are the very thin skins from a fetal or premature calf ( a slink) and are the calfskin choice for the snareside. Often , on old drums a standard head has been used because of the expense and rarity of slink skins. I don't think they can effectively be repaired, if heavily damaged but have had some success, stitching small tears,as above with very fine super strong thread( linen or koratron or gel spun polyethylene) and then cementing a patch of very thin plastic, such as some polycarbonate shrink wrap. This is commonly used for many packaging applications and is regularly tossed or recycled.