Why a picnic drink can still tip
A wider footprint is not a ground anchor.

Smooth folds
Fabric ridges can lift one side of the base. Recheck after someone shifts the blanket.
Check conditions
Wind and people moving around the blanket can disturb open drinks. Put them away when the spot is unsuitable.
Clean after the outing
Hand wash away dirt and residue and let the holder dry. Do not use a dishwasher to shortcut cleanup.