Problem converting 'even though' clause to 'despite' clause: 'Despite losing...'

I stumbled across this question in 'Intermediate Language Practice' by Michael Vince: 'Even though they were losing at half-time, City won in the end. Despite________________________________'

The answer given is 'Despite losing at half-time, City won in the end.'

For me, the answer doesn't work. Something like 'Despite being behind at half-time...' would be better.

However, I am having trouble explaining why it doesn't work. Is it because the tenses for 'lose' and 'win' do not agree in the original 'even though' sentence so there is ambiguity when you try and reduce 'were losing' to 'losing' because the 'won in the end' makes us read the subordinate clause as 'they lost'?

Solution 1:

The ambiguity arises in OP's rephrasing because in his version, [despite] losing could also mean having lost (a "completed", not a "continuous" action). The easiest way to avoid this is...

Despite having been losing at half-time, City won in the end.

The reason we don't normally use the above form is more fully explored by this answer on English Language Learners - basically, it's the horror aequi principle: we don't like multiple occurrences of the same linguistic element (in this case, two -ing forms) in close proximity, particularly when they're performing different syntactic roles. But in this case we must do it, to avoid ambiguity.

Note that in principle it could be changed to Despite being losing at half-time, but that really would be “The horror! The horror!” (originally Proust, but better known to many as Kurtz's final words in Apocalypse Now).