It appears that this change was not originally on the part of the Church, but on the part of the governments on whom the Church had to rely to carry out the secular sentences (the executions). As I recall, it wasn't until this century that the Catholic Church stopped saying that the governments of historically Christian nations had a responsibility to hunt down and punish heretics in their nations; but governments had stopped supporting them long before.
The short answer, then, is this: the Church stopped sanctioning these punishments because it knew they weren't going to happen.
Note, now: the Church wasn't the party responsible for the first of these laws, and not every official or teacher in the Church agreed with them at first. Christianity itself, from the late first century to the early fourth, was not the most legal of organizations; and people were executed for belonging to it, not for falling away from it.
Laws imposing penalties on those convicted of heresy by Church tribunals were often created not by the Church's direct or indirect pressure on government, but by powerful rulers who had very strict personal interpretations of Christianity. The Roman emperor Theodosius I, with his two co-emperors, passed the first anti-heresy laws (apparently on his own and without any sort of political pressure). The 1911 Encyclopedia Britannica discusses these:
The fifteen penal laws which this emperor issued in as many years deprived them of all right to the exercise of their religion, "excluded them from all civil offices, and threatened them with fines, confiscation, banishment and even in some cases with death." In 385 Maximus, his rival and colleague, caused seven heretics to be put to death at Treves (Trier). Many bishops approved the act, but Ambrose of Milan and Martin of Tours condemned it.
In particular, Bishop Priscillian of Avila had been engaging in practices and teaching things which a synod of local Hispanic bishops declared heretical. When Priscillian appealed to Emperor Maximus to regain his status (perhaps by putting pressure on the Pope?), Maximus had him and six companions executed on charges of sorcery. Priscillian's accusers were in turn excommunicated not only by Ambrose of Milan, but by the Pope as well. Ambrose and Pope Siricius did believe Priscillian to be a heretic, but also believed that capital punishment was somewhere between unnecessary and outright evil.
Similarly, Henry V of England was a very firm Catholic who in 1414 enacted a law against heresy—under which he executed one of his old friends. The law (and two predecessors, enacted by Richard II in 1382 and by Henry IV in 1401) was primarily designed to wipe out Lollardy, which was seen as a threat to public order in light of its association with the Peasants' Rebellion (which was at most vaguely related to Lollardy). All three laws were repealed by 1553, but re-enacted in 1554 under Mary, Queen of Scots, who used them to try to re-establish Catholicism in Britain. They were re-repealed after her death.
Admittedly not all laws against heretics were of this sort; still, it does appear that (especially several hundred years ago) rulers were not only more powerful as individuals than we're accustomed to seeing today, but also more apt to put their personal religious views into law. The Church was happy to take advantage of this; Thomas Aquinas, for example, fully agreed that heretics ought to be put to death (after, as he carefully pointed out, being allowed multiple opportunities to recant):
With regard to heretics two points must be observed: one, on their own side; the other, on the side of the Church. On their own side there is the sin, whereby they deserve not only to be separated from the Church by excommunication, but also to be severed from the world by death. ... On the part of the Church, however, there is mercy which looks to the conversion of the wanderer, wherefore she condemns not at once, but "after the first and second admonition," as the Apostle directs: after that, if he is yet stubborn, the Church no longer hoping for his conversion, looks to the salvation of others, by excommunicating him and separating him from the Church, and furthermore delivers him to the secular tribunal to be exterminated thereby from the world by death.
After the Reformation, and particularly after the European Wars of Religion, governments seem to have been less likely to want to cooperate with ecclesiastical authorities in this way; and eventually the Church seems to have stopped expecting it. The Catholic Encyclopedia, written in 1909, states:
The present-day legislation against heresy has lost nothing of its ancient severity; but the penalties on heretics are now only of the spiritual order; all the punishments which require the intervention of the secular arm have fallen into abeyance. Even in countries where the cleavage between the spiritual and secular powers does not amount to hostility or complete severance, the death penalty, confiscation of goods, imprisonment, etc., are no longer inflicted on heretics.