The age-old adage "the dose makes the poison" applies here. With ingested medications, dosage is more simple to conceptualize: how much did you swallow. With topical creams: how much did you apply. But with swish-and-spit oral solutions where a copious amount is applied topically then disposed of, it's the DURATION of application that determines dosage more than anything.
This certainly applies to chlorhexidine gluconate. Do not use it in larger quantities, for longer time per application, or more frequently than instructed.
One of many resources that state this is the U of M:
Do not use this medicine in larger or smaller amounts or for longer than recommended.
Aside from chemical irritation and other problems, chlorhexidine can stain teeth in long-term use.