Hi,
If you set a tax override zone in a shipping method, and that shipping method is the one selected on the checkout (or preselected), then this zone will be used for tax rules. If you have no tax rule matching with that zone in System>Taxes, then no tax will apply, not only to the shipping fee but also to the products in the cart.
So, it could well be a cause for no taxes showing up on the frontend in some cases.
Turn off temporarily that shipping method and see if you still have the issue on the frontend. If so, then the problem doesn't come from this.
I would recommend starting with the checks mentioned here:
www.hikashop.com/support/documentation/3...ion-listing.html#faq
If that doesn't help, create a new thread explaining the situation with some screenshots of the tax rules, the tax section in the HikaShop configuration and the URL of the shop would be the next move.