What is the maximum number of infants allowed on a flight?
Since the question was only referring to infants, my answer treats them as a subgroup of SCPs (Special Categories of Passengers). SCPs are Persons with Reduced Mobility (PRMs), infants and unaccompanied children, deportees, inadmissible passengers, or prisoners in custody.
EASA's CRD containing the comments received to NPA 2014-01 has the following statement regarding SCP in chapter 2.5:

The Agency’s NPA did not establish a maximum number of SCPs on board an aircraft. The NPA proposed to clarify the existing AMC (AMC1 CAT.OP.MPA.155(b)) relating to the operator’s procedures that the number and subcategories of SCPs should not exceed the number of passengers capable of assisting them in case of an emergency.
In addition, the NPA proposed a new GM (GM4CAT.OP.MPA.155(b)) that clarifies  that  those passengers, who could assist the SCPs in case of an emergency, should not have another responsibility on board.

It's the closest I could find on this topic. Read the whole NPA, as it is a generally interesting read on SCP considerations (for example if using the word passengers or persons is more adequate to refer to the individuals on a plane).
Essentially, the CRD goes on stating that:

The  AMC  referring to operators’ procedures to establish the maximum number of SCPs has already been adopted by the Agency in 2012 and is based on the JAA Guidance Material.
Following the recommendations from the TÜV Rheinland study, the Agency does not propose any additional limits.
This  CRD  proposes a new  GM  (GM4  CAT.OP.MPA.155(b))stating that  a passenger capable  of assisting in case of an emergency means a passenger who is not an SCP and has no other role or private  responsibility  that  would  prevent  him/her  from  assisting  the SCP.  For  example,  an  adult travelling alone has no other role or private responsibility, unlike a family travelling with children.

In the US, I would assume that due to legal constraints originating on discriminatory aspects, there is also no hard limit as to how many infants are allowed on a flight, and the decision is left with the airline association and the NAA, with existing physical and safety constraints.