It has become customary to sing יָמִים עַל יְמֵי מֶלֶךְ תּוֹסִיף שְׁנוֹתָיו כְּמוֹ דֹר וָדֹר in honour of the senior Rabbinic speaker at a function.
An explanation is given here.
The Pashut explanation given by Rashi on this passuk is that Dovid Hamelech is asking Hashem that even if it has been decreed that he die young at the hand of his enemies, Hashem should remove that decree and grant him the full 70 years of every generation.
I feel that it must be very worrying for the person for whom it is being sung because it may indicate that he needs to have his days lengthened and remind him of his mortality.
Is it a good thing to sing?