iMessage photo can’t be download

Hi there holarbayo,

If you select 'Tap to Download', do you get an error message of some kind? Since your network connection can affect this, does this happen when your device is connected to multiple networks?

Let's also be sure that you have enough available storage on your iPhone since that can be the reason these images won't download. Here's some information from How to check the storage on your iPhone, iPad, and iPod touch that can help you do this:

If your device is almost full and can't free up space, you might get a Storage Almost Full alert. If you see this alert, you should check the storage recommendations or you need to offload some less-used content like videos and apps. 

Cheers!