Deciding whether an annual insurance payment is worth the cash-flow hit

Our insurer offers a meaningful discount if we pay the full annual premium upfront. We have the cash, but paying it all in one month makes the emergency account look uncomfortably thin until the next few paychecks arrive. I'm trying to compare a guaranteed discount with the value of keeping liquidity. Do you treat annual insurance like a sinking-fund expense saved throughout the previous year? That seems simpler than making the decision from scratch every renewal.