With the latest form code update by MailChimp, there is a field added which helps lessen spam registrations. This code also affects HC to not functioning well with your MailChimp.
A workaround would be to change the specific code, see below for the sample code fomr MailChimp (naked form)
<!-- Begin MailChimp Signup Form -->
<div id="mc_embed_signup">
<form action="" method="post" id="mc-embedded-subscribe-form" name="mc-embedded-subscribe-form" class="validate" target="_blank" novalidate>
<div class="mc-field-group">
<label for="mce-EMAIL">Email Address </label>
<input type="email" value="" name="EMAIL" class="required email" id="mce-EMAIL">
</div>
<div id="mce-responses" class="clear">
<div class="response" id="mce-error-response" style="display:none"></div>
<div class="response" id="mce-success-response" style="display:none"></div>
</div> <!-- real people should not fill this in and expect good things - do not remove this or risk form bot signups-->
<div style="position: absolute; left: -5000px;"><input type="text" name="b_ad2554925dfccd2592a9f3720_d4f00e3ee6" value=""></div>
<div class="clear"><input type="submit" value="Subscribe" name="subscribe" id="mc-embedded-subscribe" class="button"></div>
</form>
</div>
<!--End mc_embed_signup-->
With that given, you have to look for (see below) the code and change the field type from "text" to"hidden", I have marked the text as bold
<!-- real people should not fill this in and expect good things - do not remove this or risk form bot signups-->
<div style="position: absolute; left: -5000px;"><input type="text" name="b_ad2554925dfccd2592a9f3720_d4f00e3ee6" value=""></div>
After changing this, your form should work now and will get new subscribers registered.
If you're still having the issue. send us a ticket in helpdesk so we can investigate.