At what point should we stop offering equity as part of compensation?

There is only so much equity to go around and there is no requirement that you distribute equity to mere employees / ICs (i.e., those not contributing capital) in the first place. If your budget does not allow you to actually pay people, and you are left exchanging sweat equity for their services, you may need to pound the pavement and raise some money. You may never want to stop offering equity, at all, as part of a compensation package, but "when," chronologically, you may want to adjust your current practice will depend on your business model, number of employees, budget projections, participation rights, and a host of other factors not present in the information you've laid out. At a minimum, you may want to explore distributing profit interests vs. voting interests and, again depending on your market strategy, reserve all interests to those who will presumably be around long enough to enjoy the windfall of a buyout. Speak with local counsel to get actionable advice on your corporate legal matters.