Since United PR hasn't yet addressed the issue here, I thought I'd share what they told me after I'd filed my column. UA has a separate budget for paying partners for award seats and is very careful not to exceed it, because then it has to take money from somewhere else.
Let's take LH as an example. If the same number of award seats are redeemed by MP members on LH as are redeemed by M&M members on UA, no money exchanges hands. But if more MP members get seats on LH, then UA has to pay LH the balance, which is usually what happens. So UA has to estimate how much of its partner award budget it can afford to allocate for LH -- or how many award seats are likely to be redeemed by MP members on LH during a certain period (not sure if they do it monthly or quarterly).
Based on my own observation, that estimate is lower than reality, and UA knows that. So it limits access to LH seats preemptively at the beginning of the budget period by removing entire routes from the availability its agents can see. If toward the end of that period it determines that it has money left -- apparently that happens often since blocking LH is so massive -- it opens up certain flights. For example, I noticed that many flights in January (beginning of a new budget period) are blocked (including FRA-MUC), but flights at the end of December (end of period) have opened up.
I'm not sure how the fact that M&M includes several airlines factors in this whole game. As many have noticed, OS is rarely blocked -- in fact, often when you try to get FRA-CDG, for example, agents tell you that you have to connect in VIE.