Much of this depends on whether and how much these clients pay you and/or your firm for the product, for support, and/or for a subscription. That said, I'm assuming they pay something and that these are products they use for professional purposes (as opposed to something for entertainment purposes, although I'm not sure that would change the answer here).
Your overall strategy:
The week on / week off schedule sounds unreasonable. I understand that multi-tasking is found to be less productive and keeping a singular focus makes for more productivity. However, it does not sound like anyone is expecting you to hop back and forth between projects with cat-watching-a-tennis-match level frequency. I don't think many people would be very thrilled with a company or individual who has a week-long response time as a policy (even if it is only temporary with the current projects). The more the customer pays / the more it is central to a part of the customer's life, the more unreasonable that becomes.
In the future:
The problem isn't that you want to focus on what you need to do for your deadlines, the problem is the inflexibility with which you pursue that goal. It is not believable that you can't structure into your schedule some time for "Customer/Product Maintenance." Whether that turns into an hour a week or an hour on M/W/F (again, not knowing the frequency of these calls, the nature of the problems, etc, makes this just a random estimate), or maybe 30 minutes, after lunch, every M/T/W/Th/F, is up to you and your manager and the nature of the work. But zero minutes to customers who have already purchased your product or services (or are in the middle of a contract to obtain them, etc.), in favor of other customers, period, for an entire week, is simply not okay.
So step 1 is to figure out how and where you can work whatever duties of customer care you have into your calendar (I'm assuming the support staff would handle many/most calls, but if there is a specific issue, you're consulted or the customer is forwarded to you). Next step is to figure out a new process for handling such situations. This is likely to include the support folks and your supervisor.
One idea is to use implement an email scenario through which you can send meaningful "away" emails (basically, vacation responses). Ideally, these would include a brief and straightforward explanation of why a response from you may be delayed (please not for a week, though!), somewhere else they can call (if applicable), some typical troubleshooting processes they can execute to see if the problem can be solved or at least isolated, and then a closing that reiterates that their concern is important to you/the firm and that you will get back to them ASAP. This will solve the issue of the tech support folks mistakenly forwarding calls/emails/issues to you while you are focused elsewhere.
If your email client can't do that, consider asking your supervisor if you can get another company email address. That way, client A has [email protected] while client B has [email protected]. If you're working on client B's project, then John.Doe@ gets the auto-reply message and vice versa.
Your current problem:
Your only choice is honesty. I'd be a little more apologetic than the other answer suggests, as this is nonetheless a customer-based interaction and, unless they are submitting questions like, "How do I right-click?" or some other asinine and frivolous inquiry, then it really isn't his or her problem what else you have going on. That's on you and, ultimately, your supervisor.