Hi and welcome. It would help us if we knew where (city/state) the plant is growing. I'm in Florida and have a large plant of the same kind.
Off the top of my head, your first picture shows where a whole bunch of old stems have been cut off, and the leaves you show in that picture look like all new growth. This might explain why it is blooming sparingly, and rather late.
Do you know if it has had any fertilizer this spring? IF it was pruned back a lot last winter, (looks like it) that would be critical to getting it going again in the spring.
My plant is a very large shrub, almost a small tree. I haven't ever pruned it back that much so it keeps on blooming pretty consistently for most of the year.
With all that healthy new green growth, I wouldn't worry too much about the dying branches. Just tell your grandmother not to let anybody prune it for the next year or two.
