Removing images in the reply messages is standard behavior for the Mail App on all iOS devices, such as iPhones and iPads.
Supposing that the recipient has already seen the images in the originally sent email, the Mail App removes them in the reply email.
As a signature owner, you might want to prevent this from happening and it can be easily done by changing these Mail app settings:
Settings > Mail > Include Attachments with Replies > Always
Or, following these simple steps:
Go to Settings
Set the Include Attachments with Replies setting to Always.