Don't confuse a progressive tense-form (a FINITE verb-form) with a gerund or present participle - forms that all full verbs possess without exception.
The sentence you cite is rather ambiguous: it could mean either
1) I no longer saw (i.e. met) the Prime Minister, and this made me sad.
2) I was unable, on account of lateness, to see (lit.) the Prime Minister.
Either way, 'seeing' is a gerund here.