The lifetimes and decay channels of ultralong-range Rydberg molecules created in a dense Bose-Einstein condensate (BEC) are examined by monitoring the time evolution of the Rydberg population using field ionization. The Rydberg molecules, which contain tens to hundreds of ground state atoms within the electron orbit, have lifetimes of ~ 1 to 5 µs, their destruction being attributed to two main processes: formation of Sr2+ ions through associative ionization, and dissociation induced through L-changing reactions. The observed loss rates are consistent with a reaction model that emphasizes the interaction between the Rydberg core ion and its nearest neighbor ground state atom. The application of this model to earlier measurements of strontium dimer lifetimes at lower densities is discussed..