The American Mathematical Monthly goes back a long way, to a radically different era in mathematical life, and has never quite caught up with the present in terms of making information readily available.   Not being a research journal as such, it mostly falls outside the realm of review databases MathSciNet, Zentralblatt.  I guess the assumption used to be that you would have a shelf full of back issues in your office for frequent perusal.   Also that you were probably involved mainly in undergraduate teaching and relied on the Monthly for your doses of real mathematics and mental stimulus.   There is some online publication now, but only for members.  


Having written articles and problem solutions that appeared in the Monthly, I am aware of the searching problem.   I've lost track of solutions I wrote, for instance, and can probably never expect to locate them.   For older main articles, JSTOR does provide some help.    But the problem section is more problematic to search over time.   (I wonder whether anyone in the MAA leadership is listening to such concerns?)  Its a large membership organization but not as useful in the modern era as AMS has tried to be.