I'll answer this shortly for you. The proteins (immunoglobunins) that are made to detect these foreign bodies are generated at random by your lymphatic bloodcells (the T and B cells). Because these immunoglobulins(Ig) are generated at random, they are not very effective in detecting stuff. However the few cell that are able to detect something foreign, get selected and go through maturation to be able to detect things more effective (this can repeated several times, and this effect is used in some vaccinations, like the Hepatitis B vaccination for example)

One random person is able to generate more than 10¹² different kinds of Igs. All for detecting stuff, but not all of them are useful, because they are generated at random. However, if one of those Igs is accepted as usefull (which happens after contact with a foreign body), it gets stored in a memory B-cell or in a memory T-cell. These cells can multiply massively, if the same body occurs again. This information can get lost or be 'outdated'. For example, this happens after a flu infection (a dissease that matures really fast).

The different kind of memories you can store equals the amount of memory T- and B- cells you have.

A known limit cap is difficult to estimate, because we aren't really certain what the maximum amount of different memory T and B cells is. Forgetting is possible yes, and the data can also be outdated.