Thanks for your message, I would be happy to offer you some suggestions for this. By default, most banners will be re-sized when switching to the mobile theme of your shop, that said it may be something we can look into with you further. Are you using a Shopify theme or a third-party theme for your shop? If you are using a third-party theme, I would recommend reaching out to your theme developer to see if they can offer you any suggestions. Alternatively, one of our friendly community members may be able to offer you some coding ideas if you are comfortable with doing that.
If you are utilizing a Shopify theme, and have available design time, this may be something that our Theme’s team can help you out with directly. If so, we’d be happy to continue assisting you through live chat, email, or callback. Please visit our Help Center here and log in to your account to create a support request. Once you reach a support advisor and explain the issue, they will be able to check with our themes team if this is something they can support directly.
I hope this gets you on the right track, feel free to reach back out here with any questions you may have!