There are many factors in play here - firstly as you cross the periods the bonding changes from "ionic" to "covalent" - eg NaH can be considered as Na+H-; such compounds are basic, and reactive (eg to moisture, to give NaOH and hydrogen) due to the presence of H-. At the other side of the periodic table (when hydrogen is bonded to the more electronegative elements) covalent bonding becomes more prevalent - think ammonia, water etc. These are more stable - in part, the bonds are less polarised so less reactive.
On descending any group stability will be reduced. For "ionic" hydrides the other element (E) becomes more electropositive the further down the group so reactivity increases; for a "covalent" hydride the orbital overlap (to form a covalent bond) between a very small hydrogen atom and increasingly larger other atom will become poorer and poorer, so the E-H bond becomes weaker.