Two possible distant (geographically as well as time-wise) lines of events that enable the Avars to survive - and presumably if they do, their mixed Turkic-Slav state ends up as a slowly 'Europeanising' ex-nomad regime like the Magyars did in the OTL C10th.
1. No overthrow of the Merovingians by the Carolingians in 751, or a long-term division of the Carolingian state between Charlemagne and his younger brother Carloman in 768 that sees the latter survive and his sons inherit his realm - possibly as they are able to call on aid from a stronger Byz empire in Italy to keep Charlemagne's army at bay. As a result Charlemagne (who still governs N and W Francia, the Low Countries and most of Germany) is too busy with internal strife to unite the Francian lands and then attack Avar Pannonia in the 790s.
2. The Magyars were in OTL called across the Carpathians in the mid-890s by the then Byz emperor Leo VI to help him tackle the expanding Bulgarian state in the Balkans (based on the lands of modern Bulgaria plus Serbia plus Wallachia N of the Danube) by taking them in the rear - from the NW. At this point, the Bulgars are pressing the Byz back in Thrace and Macedonia. For the Bulgar threat to be met by a Magyar attack in their rear, the Byz needed the Magyars to be in control of what is now S Hungary and ready to attack via the Belgrade-Nis route, so they would be evicting or suppressing the Avars in Hungary first - and the Avars had always been long-term foes of the Byz since the 570s and had long coveted the inner Balkans so a Byz-Avar alliance against Bulgaria was unlikely.
If the Bulgars (based in Wallachia on the steppes in the mid-C7th) do not migrate successfully S of the Danube in 680 and push the Byz back to the Haemus range, which would result from a stronger Byz army better led and less Arab pressure on them at that stage, or if the Byz under the hugely capable and ruthless Constantine V defeat the Bulgars in the 760s-770s, the Bulgars are suppressed or evicted. In OTL, the Byz campaign to stop them in 680 failed, possibly as a lumbering Byz army with inadequate cavalry or supplies could not catch mobile nomads or the latter hid in the marshy Dobrudja - and emperor Constantine IV caught malaria and went home (he died aged c. 34 in 685 so could a stronger man win the war??). No major Bulgar state in the Balkans by the later C9th; no need for the Byz to call in the Magyars; a surviving Avar state does not get attacked across the Carpathians. Probably its Khagan gets forced by a stronger Christian neighbour - a Catholic surviving Bavarian state backed by the Papacy or an Orthodox Byz ruler - to convert to Christianity and slowly become a semi-feudal Europeanised king once the Bavarians or the Byz are strong enough to enforce this militarily - once the regional Avar nobles start to break away from the Khaganate and central royal power declines?
