Automatic syncing of Shopify data is only active for shops on a paid plan. While on a free plan, you may test any updates to your shop with a manual resync, using the relevant link at the bottom right of the Landed admin.
Shopify can take up to a few minutes to notify Landed of any changes, and Landed itself can introduce some delay when under heavy load. If you've been waiting an unusually long time (an hour or more) and your Landed sites have still not updated, you can try a manual resync, as described above.
Note that a full manual resync needs to synchronize every collection and product in your shop, so depending on the size of your shop, this may take some time and should only be used as a last resort. Your sites will not be affected by any downtime as a result of this process.
Currently, collection updates are unreliable. This is due to a bug in Shopify’s API and is beyond our control.
Update 2016-12-03: this appears to have been fixed on Shopify’s end.