Approximately early July to mid-October.
Via Valais season starts when the huts open, but more importantly, when some key bridges are put into place for the descent to Randa on Stage 7. Without these bridges, it is not possible to cross a steep gorge. You'll need to check the Topali Hut website for the dates.
The end of the season is similar - it's when the huts close and the bridges are removed. See our Via Valais SERVICES page for hut links.