While EZ Inventory's most frequent scheduling option is Every 1 Hour, you could potentially update your Shopify inventory more frequently than this if you don't have that many products/variants by creating multiple Data Feed configurations with different settings for the "Minute":

Non-Shopify Plus stores can expect roughly 5,000 total variant updates per hour (10,000/hour for Shopify Plus stores as they have a higher API rate limit).

So if you have less than 1,000 total variants in your store, for example, then you could update your inventory every 15 minutes by duplicating the Data Feed configuration and creating 4 separate ones where the "Minute" settings are set to 00, 15, 30, and 45.