If you're sitting down to work and your brain is telling you that you can't get anything done in 20-30 minutes ("or, at least, nothing that constitutes meaningful progress" to quote my brain), one of two things is happening. 1) Your brain is totally, 100% lying through its teeth. This happens all the time and is the basis for procrastination. 2) Your brain is tired and telling the truth -- you don't have the mental resources to focus right now. This happens to me after about 60-90 minutes of concentration, and it takes 20-30 minutes of "lightening up" to recharge. (Note that these numbers are taken in the absence of major stressors like babies and in-laws. You may also need to eat, sleep, or perform some other kind of self-care to recharge.)

In case (1), it's fun to imagine that your brain is maliciously lying to you about the progress you'll be able to make, but it's more ignorance than malice. Get good at recognizing the real obstacles and talking yourself through them. Is there some key piece of understanding you're missing, or some design problem you couldn't solve in your head? When you have to go long periods during your day without access to your tools, you'll build up questions that you need the Internet, a computer, or pen and paper to answer. Remember what they are; don't just unconsciously make assumptions or treat these questions as unanswerable. Another mental blocker besides lack of understanding is worrying prematurely about the properties the finished product must have (it must be good, it must be well-written, it must look beautiful, it must be a complete treatment of the subject, etc.). Another blocker is stacking up tasks in your head so that one blocks another -- I don't want to do B until I've done A, but I don't have the mental energy (or other resource) to do A right now, but I should just force myself to, but I can't... These blockers will dissolve once you recognize them and look at them properly. If you feel any resistance to working on a task (whether it's a short, 20-minute task or a longer task to make progress on), immediately ask yourself why.

It's particularly frustrating, for example, if a 20-minute task is put in the front of your queue, ahead of your "real work" that constitutes "real progress." A bug pops up, or a configuration issue with your computer, or an urgent email, or a git conflict. You thought you'd have just enough time to implement and test feature X, which is just a one-line change, and now there's no chance. There's not much to do about these things except to recognize them, and to adjust your definition of "real work" and "real progress" to account for them. If you were going to use the time to dump ideas, code, or text from your head, dump notes into a text file for a couple minutes.

Don't get me wrong: the limits of 20-30 minute work blocks are real and not all in your head. You can go to far-off places when you have hours to immerse yourself in something, and in addition, just the knowledge that you have this time seems to unlock creative thinking. However, don't believe everything you hear about what's possible in 20-30 minute chunks either.

I'm writing about time management generically or from the point of view of a programmer, but it depends on the nature of the task. I've never worked closely with a PM, so I don't know what sorts of tasks we're talking about. 20 minutes sounds perfect for answering an email or two that doesn't require too much writing. When I have to write a longer email or a design doc, blog post, etc., I write in my head while doing other things and then dump it out, or I dictate into a voice recorder (which is valuable for getting ideas out whether or not I later listen to the recording).

I echo what others have said about keeping your work windows open on your computer, and keeping a log of ideas and what you're going to do next when you come back. Hope this helps.