Plausability Check: Spanish Habsburgs

Just out of curiosity, do the Habsburgs in 17th century Spain have a shelf-life or is it possible that they could survive longer than they did? For instance, would the survival of Baltasar Carlos and him having children butterfly their extinction or simply delay it?
 
Stop the inbreeding and they have a decent chance. Or just get the stable hand in to the queen's bedchamber to resolve the problems.
 
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