How long would RSV typically last in an infant?

Depends. Typically the symptoms of RSV peak after the first few days before getting better. Usually infants improve somewhere between 5-10 days; however this can vary widely, and it is not uncommon for the cough and wheeze to last several weeks after the initial symptoms began.
7 - 10 days. Rsv infection typically induces heavy runny nose followed by fast breathing, wheezing, and chest congestion in otherwise healthy full-term born infants.