The patch failure may not be due to erosion but instead due to subsidence -- settling of poorly-compacted soil in the excavation. An easy, reliable way to avoid subsidence in a narrow excavation is replace the native soil with something else more easily compacted (gravel?) or less susceptible to subsidence. The water leak itself may also have caused subsidence in an area larger than or deeper than the repair zone.
Occasionally I core drill a hole in a city-owned road and vacuum excavate a hole to precisely identify the location of a buried utility. The city requires me to backfill with "flowable fill," also known as "controlled low strength material." In layman terms: weak concrete. I mix sand, water, and a bit of portland cement. Sand and water alone aren't very interesting, but when cement is added, the mix turns into something that pours. There's an admixture powder I add too which causes more air entrainment during the mixing; this makes the "mud" pour and flow really nicely (but it's not strictly necessary). The idea is that this this flowable fill goes in dense, fills every little void, is quick to install, and has extremely little potential to settle, but is weak enough it can be re-dug later if necessary - though it often is harder than native soil.
A technique used for asphalt repair after some excavations is called a T-patch. The asphalt is cut larger than the excavation by 6-12 (or more) inches so that the cold joint between new and old asphalt is not directly above the edge of the excavation. This helps reduce cracking/breakage along the joint or in the case of minor subsidence.
A product called "tack coat" can be applied to the cut edge of the original asphalt to improve the bond between the new and old. It also can be spread over the top of the joint to help seal the crack. I don't know if it is available in a small pail though: two weeks ago I used most of a 5 gallon bucket on maybe 120 lineal feet of hot asphalt patching; a bucket this size is far more than you'd need.
TLDR: you can re-dig and do it right (better compaction and/or better fill material) or you can leave it alone to settle/compact naturally, perhaps applying more asphalt or patch material on top as needed due to the settling.