> Berjast þeir lengi svo að eigi verða umskipti.
> They fought-each-other for-a-long-time so that changes happened not.
(there was no outcome)
When, as here, it doesn't have a causal sense, you can often translate
'svo að (eigi)' as "with(out)" + a present participle: "They fought
for a long time without any changes / with neither side gaining the
upper hand."