There's a fundamental flaw hiding under arguments like yours: the "civilization" you're circumscribing is an imaginary and arbitrary boundary. An ahistorical retcon. It's as unsupported as discredited racial theories that all humans fit into three tidy buckets ("caucasoid", "mongoloid", "negroid").
For example, maybe you're talking about "Christendom". But then it's not actually in decline -- hispanics are part of Christendom, and Christianity is growing in Africa, so on net it's growing, not shrinking.
Maybe you mean the population within the actual geographic boundaries of Europe and the former British colonies (including America). But if that's your definition, then you would accept immigration as a solution, and you would admit that America is already doing fine.
Maybe you're talking about people who live in societies with constitutions that ultimately derive from the ideas of the enlightenment. But again, not shrinking.
Maybe you're talking about a specific local cultural tradition -- but then it's not really "the West" that's in decline. "Western civilization" necessarily spans a huge range of cultures, otherwise you can't successfully take credit for everything from Socrates to Charlemagne to Descarte to Luther to Newton to Einstein. Consider the magnitude of the cultural turnover across that span!
Is South America part of "Western civilization"? It's literally in the western hemisphere and colonized by Spain and Portugal. If you're really talking about having a connection to European cultural history, it clearly fits. But if we include it, then again the decline disappears. Guatemalan immigrations to the US can't be a non-western invasion.
What it boils down to is, people use "western civilization" as a cover for "white people just like me". But there's no non-racist way to equate that with "civilization".
Our civilization -- the actual web of relationships and institutions that keep the lights on -- is clearly doing fine. That web is fundamentally global, as much as that annoys chauvinists. And globally, the world is getting richer and more equal at a rapid pace. Mortality is falling. The population is not in decline, although it has a good shot at plateauing in the coming decades, which will be a good thing.