Does the prayer become invalid by the discontinuation of sequentiality (muwalat) if the worshipper pauses for a short while after reciting one verse of Al-Fatiha before completing it, and what is the permissible duration to avoid the discontinuation of sequentiality?

If the silence after reciting a verse from Al-Fatihah is an ordinary silence, like the duration of a pause, or a brief one, then there is no harm in it and it does not break the continuity; because pausing at the end of verses is a Sunnah (definition) of recitation. Brief silence is that whose duration is short and does not give the impression of interrupting the recitation or turning away from it. As for a long silence that gives the impression of interrupting the recitation and the reciter turning away from it, it invalidates the recitation and necessitates re-starting Al-Fatihah.