Does bleeding caused by the IUD mean that one cannot pray?

Firstly: 

The basic principle concerning the blood that comes from the
woman is that it is menstrual blood, so long as the bleeding has not lasted
for longer than fifteen days, after which it is istihaadah (non-menstrual
vaginal bleeding) according to the majority of fuqaha’. According to some,
it is menstrual blood so long as it has not lasted for longer than one
month, after which it becomes istihaadah. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: 

If the strength of the opinion that there is no minimum or
maximum limit for menses is established and it becomes clear that this is
more correct view, then it should be noted that every time the woman sees
natural blood for which there is no cause such as an injury and the like,
then it is menstrual blood, without specifying a particular time frame or
age, unless it is ongoing and never stops, or it stops for a short time such
as one or two days in the month, in which case it is istihaadah. … Shaykh
al-Islam Ibn Taymiyah said: The basic principle concerning everything that
comes out of the womb is that it is menses, unless there is evidence to show
that it is istihaadah. He also said: Whatever happens of bleeding is menses,
so long as it is not known whether it is bleeding from a vein or an injury.
Just as this opinion is the stronger one in terms of evidence, it is also
easier to understand and to act upon and apply, than what those who put a
time limit on it suggested..

End quote from Risaalah min ad-Dima’
at-Tabee‘iyyah li’n-Nisa’

Secondly: 

The length of the period may increase and decrease, and it
may come earlier or later. The blood that comes out in these cases is deemed
to be menstrual blood. A woman’s period may usually be seven days, but it
may last as long as ten days, for example. Thus the ruling in both cases is
that it is menstrual blood.  

Thirdly: 

Insertion of an IUD usually causes disruption in the
menstrual cycle, making it longer or causing it to come earlier or changing
the nature of the menstrual blood. 

Based on that: 

The blood that you are seeing is menstrual blood and it is
not acceptable to pray and fast at this time, even if it lasts longer than
the usual period, so long as it does not last longer than fifteen days
according to the majority view, and does not last longer than a month
according to the other view, after which it becomes istihaadah. If it lasts
less than fifteen days, it is menstrual bleeding. 

The view that the bleeding that occurs with the IUD is not
menstrual blood at all is an opinion for which there is no basis. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was
asked: There is a woman who had an IUD inserted. Before that procedure her
period was seven days, but after that her period increased to ten days.
Please note that on the seventh day the bleeding decreases, then on the
eighth and ninth day the bleeding gets worse, then it stops after the tenth
day. 

He said: She should carry on until she becomes pure. 

Questioner: Is it part of her period? 

Shaykh: Because this IUD changes the period, because it
restricts the flow of the blood out of the uterus, and the blood flows more
slowly, so the period becomes longer.

End quote from al-Liqa’ al-Maftooh, 227/27. 

And Allah knows best.