I don’t think there is a problem with obtaining consent once as long as your disclosure is clear as to what it applies to and your system is equipped to retain the information. Also, you should tell the customer how they can withdraw consent and future disclosures should comply with the format of your demonstrable consent – if you change the hard/software needed to access or retain the documents then you need to need to meet certain re-disclosure requirements. Also consider that customers might not like this – they might prefer to have the option of paper or electronic.
Here’s a link to the E-SIGN Act disclosure requirements (7001(c)): https://www.bankersonline.com/regs/esign/esign.html