From what I've read and researched. Vikings appear to mostly be successful through their raids and impact of their culture on the British Isle. However when it comes to actually defending the lands they managed to conquer. Northumbria, east anglia, I believe are some examples. They were obviously all conquered by English kings. An example of a strong viking army that comes to mind would be the great heathen army. That managed to defeat the kingdom of mercia then go on to take Alfred the Great by surprise at his own capital...it appears that the army used the viking tactic of surprise on the enemy. Instead of an open pitched battle, to great success. However although the obvious reason for the army not committing to an open field battle being. Well they didn't need to. Was it also possible due to them questioning if they were able to fight and win against an Anglo-Saxon army under the command of Alfred? Because guthrum went out of his way to bribe people to not announce his army's arrival so he could ambush. I find this interesting. Because at a later time Alfred the Great goes on to defeat the great heathen army. Also I believe his son Edward The Elder deafeated northumbria around 910AD. Also the the reinforcement sent to aid guthrum and his army against Wessex were defeated at Devon when the peasantry sallied out from their fortress and fought the vikings openly and surprising the vikings lost. My question is that we're vikings just less successful at battles and was this a big factor in there eventual downfall? because this appears to be the case. Which also seems to be the reason the vikings eventually disappeared. Of course christianity was a big factor in this but. It also seems that the vikings partial inability to adapt to open field battle, army to army. Which is obviously necessary to keep control of your kingdoms. The vikings could not do as successfully compared to there Anglo-Saxon and even Irish and Scots counterparts.
If I may, I believe you are placing too much focus on battles as the decider of Viking fate.
The fact is the same societal forces that allowed large armies like the Great Heathen Army meant they were prone to conquest once settled. Unlike Anglo-Saxon kingdoms and Wessex in particular, Vikings were a decentralised society with little to bind distant communities together. Once settled and no longer on the attack the viking settlers are vulnerable. They don't have the massive infrastructure advantage of the church or the centralisation of Wessex. The Kings ruling viking lands are puppets without real power, instead patchworks of local chiefs each ruling a small territory of one or more villages is the norm. This means if an army from Wessex arrives they are doomed unless they can persuade enough chiefs to join a common cause under a common commander, a pretty impossible task. It's this reason we see Wessex gobble up territory without battles.
However, like the later English attempts to hold Scotland it is possible for the settlers to rebel enough and make control difficult enough for Wessex to hold. So though a part of England it keeps the Danelaw customs, keeps its own lords and pays much lower taxation. Northumbria still manages to rebel each time a viking army lands however right up until Harald Haadrada. It's William the Conquerer's harrying of the North that manages to put an end to Northumbria's special treatment.