Not sure how long you need to survive in the PL to stop being defined as a Yo Yo club.
Of the 20 clubs in the Premier League, Arsenal have been in the top flight since 1919, Everton since 1954, Liverpool since 1962, Manchester United since 1975, Spurs since 1978, Chelsea since 1989 and Manchester City since 2002.
Beyond those seven, the longest-serving top-flight clubs are Southampton and West Ham (both 11 seasons), Palace (10 seasons) and Leicester (nine seasons).
According to this article there is a limited ‘life expectancy’ in the Premier League for clubs like SUFC. We will never 'establish ourselves' in the PL and become like e.g. Spurs. We will be relegated eventually.
How long can a smaller club — without the heritage, power or modern wealth of the league's elite — hope to remain in the top flight?
theathletic.com