Are the Reapers on a deadline?

So this isn’t an important post/question, but it’s something that’s been on my mind while playing 3 the last few days (I played through the series when it originally came out, so I know the entire story). Something that’s stood out to me is that the Reapers get foiled by Shepard on 3 separate occasions before the third game (Sovereign, Collectors, & Arrival), and are clearly bothered by this pesky human that keeps landing solid hits on them, yet they insist on carrying out their invasion ASAP.

Is there an in-universe explanation why, after ME2, a group of immortal machines wouldn’t just go into hibernation in dark space for a century or so, letting Shepard and the rest of the generation that’s been punching WAY above their weight class die off (while the rest of the galaxy treats Shep, Anderson, and company, not to mention the people like Liara, who’d still be alive during Round 2, as discredited, insane conspiracy theorists when the Reaper invasion never happens), only to then invade under a more complacent galactic generation?

After Sovereign’s failure in 1, they’d lost the element of surprise that warping into the galactic capital had afforded them in previous cycles. Invading conventionally from dark space (like they did after the Alpha relay was destroyed in Arrival) allowed the galaxy to communicate and coordinate a resistance. Even if arrogance is the only explanation, surely machines could run probabilities and say patience was the wiser strategy. Or was it personal now and they wanted to kill Shepard themselves (rather than just watch from afar as he dies of old age having become a galactic pariah for claiming the Reapers were coming, aiding Cerberus, destroying an entire Batarian system & causing a war between the Alliance and Batarians).