The turnout at a client event depends on three factors. These are the relevance of the programme, the quality of the invitation and the timing.
Make sure you have a programme that offers value. Relations don't come for drinks: they come for an experience, knowledge or a network they can't get elsewhere. Communicate that value clearly in your invitation.
Personal invitations work better than mass mailings. Have account managers or the board invite people personally. That boosts engagement enormously. Send a save-the-date at least 8 weeks in advance and the official invitation 4-6 weeks beforehand.
Choose the right moment. Avoid holiday periods, busy industry weeks and Mondays/Fridays. A Tuesday, Wednesday or Thursday afternoon or evening often works best for business relations.
Also consider communicating limited capacity. Exclusivity increases the urgency to respond.