Word for expressing ongoing problems
It seems that a good option is to use a verb that captures the concept concisely, such a verb as "perdure" for instance.
- Despite positive temporal trends, the problems perdured/persisted until the end of the study period.
Wiktionary (intransitive) To continue to exist, last or endure, especially for a great length of time.
perdure is rarely used but its meaning fits your specification.
Despite positive temporal trends, the problems endured until the end of the study period.