Emails may 'bounce' or they can be tagged as 'spam'. When you are relying on your emails to generate business you want to be sure you receive customer enquiries and that they receive your replies.
If you wish to use a webmail contact form on your site or a section where customers can post reviews it is particularly important that this interlinks properly with your email. This is because your customers' email providers (Gmail, Hotmail, AOL) periodically alter their spam protection. This means, without proper email management, you might not receive their emails.
Gmail, Hotmail, Yahoo and all the rest are useful for general email communications but neither you nor we can control how they are functioning. You need to be sure that your primary email link to your customers (and to your earnings) is secure and at all times and fully operational.
Emails from potential customers are your hotline to income so they need special attention. Ideally this email 'hotline' should be kept separate from other correspondence; it should be checked daily and it should be properly organised, especially if you need to store older emails for your records.