It seems to me that a lance would be great for knocking someone off of their horse, or breaking through enemy lines. However, after that, I feel like it would be broken or would be yanked out of the user's hands. In other words, it seems like you could ever use your lance once. Is this correct? What happens after the knight strikes home with their lance?
You're essentially correct, lances (which are just long hardwood spears, practically speaking) could and did often break or get lost during charges, but if they helped you break up the line before you reached it then its primary job was done. When the cavalry regrouped for another attack you might find yourself at the back or middle of the formation where your (broken) lance was not as necessary as your weight and presence or you might get to reuse it if you still held it.
The purpose of a group of knights in a fully-fledged battle was to use weight of numbers to punch a hole in a packed (but ideally slightly broken) formation. The knights would then disengage and charge again until they either routed the opposing force (where having a spear is still quite useful for stabbing people), fell into a mêlée (not useful), or withdrew to recuperate, possibly rearm, and possibly rehorse. The power of knights was their mass and the immense discipline this manoeuvre required against a group of soldiers who likely lacked that same discipline. Notice that I said ideally the infantry formation would be slightly broken, this could either be due to missile support or skirmishing prior to the charge. When cavalry charged unbroken formations without support they almost invariably lost a great deal of their impetuous and were defeated.
They're not necessarily a one-shot weapon, but if they were then it wasn't the end of the world. I haven't come across any source detailing how a battle was lost because they ran out of spears for charges.
Lances did break though not as much as in demonstrations/jousting. Those lances are made to break.
Disarmament also happened, but there are techniques to avoid it. For an example, there is a technique used in current mounted skill at arms to avoid losing the lance. Essentially upon contact, you allow the lance to point downward, rotating around and then use the momentum of the horse to remove the lance from the target. My knowledge of this comes from 19th century cavalry manuals but I see no reason to suppose that medieval knights would not be able to perform a similar technique.
The ideal situation? The lance penetrates the target, the horse runs past the target and the momentum withdraws the lance.
For a demonstration see the lance sections here (obviously the situation would be different, but the principle is the same).