Well gosh, I hope we're not still praying for the souls of people who died in the Middle Ages--that's an awfully long time to be suffering the hell-like pains of purgatory!
I want to talk about a specific type of monetary bequest, called a "chantry" in England/English (Altarpfünde in German), because they're traceable in surviving sources and have been studied in some depth. Essentially, a chantry was an endowment for a priest to say Masses in support of the donor's soul, or possibly their ancestors/future family. In some cases, this could range all the way up to building a small chapel as an addition to a church, or even an entire separate chapel building. A chantry Mass would not be a standard church service like we know today with parishioners, a homily, and so forth; the point in the medieval mind (and the definition of a Mass today) is the celebration of the Eucharist.
Later medieval religion focused more and more on the quest for salvation. This meant behaving well or confessing when one did not behave well on Earth, and after death it meant speeding one's soul through the cleansing punishments of purgatory (paying back punishment that had not been worked out on Earth as assigned penance) as quickly as possibly to reach paradise.
To be clear, we're not talking about rescuing people out of hell: this is not possible in medieval theology. Purgatory is for people who will go to heaven, just, not yet. You're probably familiar with indulgences--those are essentially rewards or credits one could earn in this life to remit time in purgatory so long as they died in a state of grace and would ultimately be destined for heaven.
Chantries are a really interesting example of late medieval concern for souls after death because their timeline doesn't match up directly with some of the other big related practices. They first appear in France at the end of the twelfth century, and their proliferation is usually dated from the thirteenth century on. But intriguingly, whereas other examples of concern over death and dying well ramp up in popularity after the Black Death, the foundation of chantries actually decreases in number. The decline often seems steeper than the population loss from the first waves of pestilence, too. In Salisbury diocese, A.D. Brown found that twice as many chantries were established between 1300-1349 as 1350-1399. At St. Paul's Cathedral in London, there were 26 new foundations from 1300-1349 compared to 20 from 1350 to 1550.
So the reason for the decrease isn't related to a change in underlying devotion--in fact, the change that brought about the rise of chantries was accelerating. So we have to look to other factors to explain the drop in new foundations. In addition to the post-Black Death population depression, scholars and medieval sources alike point to another major factor: economic difficulties even amidst an overall growing European economy.
And, yes, those financial difficulties affected existing chantries, not just potential new ones.
In 1370, for example, nine of the chantries at St. Paul's were vacant. That is, the initial endowment was no longer enough to pay the wages of the priest to say the Mass, giving the rising cost of living. Cathedral canons also note a shortage of available/willing priests.
Unfortunately, we don't have much evidence as to how descendants of the people whose chantries evaporated felt about the matter. One point to note is that David Crouch's studies of medieval noble families found that it was very difficult to sustain a "family identity" over a significant number of generations. One might not have cared so much for Great-Grams' soul in an emotional or social sense.
There is also the question of "purgatorial math." That is to say, when we look at false or forged indulgences in the 15th century (yup, there was a black market in fake certificates of indulgence), the creators would assign absolutely wild numbers of years off purgatory for saying the rosary so many times or going on this pilgrimage or praying with that prayer book. Into the thousands. Official indulgences after 1400 were limited to forty days. So perhaps "in perpetuity" had a similarly nebulous meaning in the specific.
Because while we don't know about individual cases, we can see reactions to the overall erosion of chantries. Robert de Braybroke, bishop of London in the 1390s, is a good example of a common solution. He assessed the vacant and financially-precarious chantries, and determined to consolidate them into 27 group-chantries. In other words, the continuance of prayers in general was important, but they did not have to be as specifically dedicated to one person or one family.
Additionally, in the fifteenth century the prerogative to establish chantries tended to be restricted to the wealth nobility and gentry, in order to prevent recurring problems of the financial type. However, for a good chunk of Europe, there was quite another problem about to occur.
That's right: the Reformation resulted in the complete abolition of chantries in Protestant countries--with no purgatory and no need for human action to reach up to God's grace towards salvation, there was no point in praying for the souls of the dead in the same way. The endowments might be converted to pay the salary of a new Protestant church schoolmaster (many chantry priests had supplemented their ecclesiastical income by teaching the equivalent of elementary school), or purchased by a wealthy aristocrat, or even fund civic public works projects.
But (now) Catholic spirituality evolved in the sixteenth century as well, especially in its new global context with a missionary outlook. A spirituality of charity (in the modern sense of helping others with basics of life) emerged out of the spirituality of penitential suffering (for oneself, and vicariously for others). Provisioning Masses became, in general, less important for the health of one's soul. Do people still pray for the medieval dead? In the general sense, absolutely. There are plenty of opportunities to prayer for the collective dead--continuing the basic pattern demonstrated by Bishop Richard in 1390. Some browsing around the Internet will even turn up plenty of shrines and organizations offering a roster of perpetual remembrances through prayers and Mass.
As to specific surviving medieval chantries or prayers for monastery founders and patrons, most things to say would be anecdotal. However, sixteenth-century Piece of Awesomeness Ignatius of Loyola held that religious communities and schools should always remember their founders through prayer, presumably reflecting the ethos of his time. And since he did a little thing called founding the Jesuits, the idea of not just commemorating medieval patrons but praying for them does live on.