Firstly, it should be noted that not all Protestants reject the doctrine of the Immaculate Conception. It is not as though there is a uniform Protestant doctrine that strictly states the Immaculate Conception to be false (if there is I am unaware of it). Martin Luther himself defended the Immaculate Conception:
But the other conception, namely the infusion of the soul, it is piously and suitably believed, was without any sin, so that while the soul was being infused, she would at the same time be cleansed from original sin and adorned with the gifts of God to receive the holy soul thus infused. And thus, in the very moment in which she began to live, she was without all sin.
Only later did he refute his original position in the following way:
Mary is conceived in sin just like us.
On a lesser note, John Calvin and Ulrich Zwingli also appear to adorn Mary (see the link posted above). The High Anglican Church goers also seem to be fond of the Immaculate Conception. All of these are simply examples of the fact that Protestant thought need not equate to 'anti-immaculate conception'.
That being said, the following are the most predominant arguments I've seen used by Protestants against the Immaculate Conception.
The following verses are often used in arguments against the Immaculate Conception:
All have sinned and fallen short of the glory of God.
1 John 1:8
If any man says he has no sin he is a liar and the truth is not in him."
"My spirit rejoices in God my savior" (as spoken by Mary herself).
Following these verses, Protestant theology rather firmly asserts the fact of sin and that such a fact is the very reason Christ came into the world. The main theory of atonement present in Protestant theology is known as penal substitution. It essentially asserts that Christ took upon himself punishment for every sin that has or ever will be committed. So saying that a person can be without such sin suggests not only that there is a soul that doesn't need Christ's power but also that Christ's own work is not fully needed. Obviously this presents a major problem. So typically most Protestants look rather firmly down upon the idea that even the Mother of God was without fault.
ORIGINAL SIN VS. PERSONAL SIN
Although many Protestants accept the idea that there exists original sin in some capacity, the Protestant sects face a wide range of differing views on exactly what is meant by the term. Needless to say, the significance of the theological concept that is so central to Catholic and Orthodox theology (which hold that Christ offered penance for original sin more so than personal sin) suffers in importance under Protestant theological consideration. The distinction that is apparent for Catholic and Orthodox thinkers between original sin and personal sin becomes blurred and less significant. The result is, according to Catholic and Orthodox thought, an inflation of the property of personal sin and a deflation in the property of original sin. Thus when the proposition that a person is 'sinless' comes into play, it is about as heretical as one can get. But it is a statement that under Protestant theology is not only confusing, but not able to be coherently understood with the current frame of thought.
In Protestantism, to propose that one is 'sinless' is to propose one does not need a savior. But Catholicism and Orthodox Christianity break down 'sin' into two essential parts; original sin and personal sin. Original sin engenders continuously the inclination to personal sin. So in theory, a soul can be sinless in regards to 'personal sin', but such would only indicate that the same soul was unified so significantly with the grace of Christ that they did not face the consequences of original sin. There are two ways to save a soul after all; they can be saved by falling into a pit and requiring assistance after the fact, or they can be saved by being cared for and guided around the pit. The latter would be the means by which Immaculate Conception proponents would suggest Mary was both saved and free from personal sin. Mary would have been preserved from original sin by the grace of the penance Christ offered for original sin, and thus would have been reserved from personal sin.
FINAL PROTESTANT OBJECTIONS
This clarification serves to dismiss the use of the Lukean verse in hopes that it contradicts the Immaculate Conception. But Protestants could likewise point out several objections to this whole line of thought, including the notion that it would seem unfair if God could save souls from the very oppurtunity of sin that he would pass up the chance. If God could exempt Mary of original sin, why could God not exempt all souls from original sin, or more so, why doesn't he? Another objection comes at the hands of the verses already mentioned. What is to say the verses stating that 'no person is without sin' is either a) only to be taken generally or b) referring to 'sin' in a way that allows theological exceptions. These objections are perhaps the most primary responses to the actual doctrine of the Immaculate Conception.