It is disheartening when a guest does not leave a review, especially when you know they had a great stay and that you went above and beyond for them. A recent guest had so many questions and needed so much help and I was happy to give it. I even helped her when she had a problem with a cancellation situation with another booking. I was sure she would write me a glowing review (she told me should would in a message after her stay) but no review followed.
In the beginning, I used to leave a review for every guest but then was so disappointed when they didn't leave one for me, even if I sent a reminder. After all, when you are starting out, you need every good review you can get because it not only encourages other guests to book, but pushes you up the search results and is vital after your one month 'new listing' boost is over.
Now I usually only leave reviews for guests that have left one for me first. Maybe I am shooting myself in the foot if they are waiting for me to leave one for them. However, I have not found that it makes any difference in the percentage of my guests that leave reviews. Whenever I deviate from this to see if my review will prompt one from them, it doesn't work. They are either going to leave one or not and in the latter case, they are already ignoring any reminders from Airbnb.
We have to be reaistic about this. Leaving a review for you is not going to be every guest's top priority. All you can do is try to encourage them. However much you have gone above and beyond and however much it hurts, forcing guests to leave reviews is a bad idea. Some will leave an ill thought out review out of impatience and others might be annoyed enough to leave a less than 5 star review because they felt pushed.
I also don't ever ask guests for a 5 star review. It's a bit pushy. I usually don't bring up reviews with them at all during their stay, but will happily discuss it if they bring it up. Instead, I send a thank you message after check out which includes a general reminder to leave a review (but only for the non-problematic guests). I don't mention 'positive' or 5 star. It works most of the time. I'm currently at around 75% review rate and 88% 5 stars.
What should definitely change as @Sarah977 clearly explains is that hosts are measured on this percentage. It's completely non-sensical. Assess us on how many reviews we leave by all means, but don't judge us on the choices of others!