2 factors that I'd consider would be (i) how cheap and nasty (or otherwise) the existing one is, and (ii) if you can easily afford to put in a good one.
i.e. if it's a no-name piece of junk and 8+ years old, it's time for Silicon Heaven; if it's a decent high-quality one e.g. a Seasonic X-series, probably not so much (because it's less likely to fail at this age, and more importantly when it goes it's less likely to take out other things). Either way, if you can drop in a e.g. Seasonic PRIME series with a 12-year warranty and not really feel the financial hit, that's a no-brainer whatever 8-year old model you're currently running on.
(IMO, as one who views the PSU as the engine of a PC build.)
Desktop: E3-1270 v5, X11SAT-F, 32GB, RX 580, 500GB Crucial P1, 250GB Crucial MX500, 4TB 7E8, Xonar DGX, XL2730Z + L22e-20
HTPC: i5-2500K, DH67GD, 6GB, GT 1030, 250GB MX500, 1.5TB Barracuda, Xonar DX, G2420HDB