What challenges the ideasthesia balance theory has to answer?
Short answer
Ideaesthesia does not comprise a theory or even a hypothesis. It is merely a term meaning 'sensing concepts' or 'perceiving meaning'.  

Background
As Steven Jeuris also comments, ideaesthesia is not a theory, it is simply a term. It is a combination of two Greek words, namely 'concept' or 'idea', and the other is 'sensation', or 'aisthesis'. In translation, ideaesthesia means sensing concepts or perceiving meaning (source: Danko Nikolić).

It it used to denote phenomena as the Kiki/Bouba effect (Milan et al., 2013; Martinez &amp; Milan, 2015) and synesthesia (Jürgens &amp; Nikolić, 2012) as you write. These phenomena are associated with assigning shapes to names, and colors to graphemes (and the likes), respectively. As far as I can see, ideaesthesia does not explain anything, it is not an observation, it is not a hypothesis, let alone a theory. It is a term used to group phenomena where people associate seemingly unrelated concepts.

Further, for what it's worth, a cursory Google Scholar search on 'ideaesthesia' yields few hits (82), and those hits that pop up, in part referenced here, point sometimes to questionable journals or to irrelevant papers. I would hence use the term cautiously as it doesn't seem to be widely used.   

References
- Jürgens &amp; Nikolić, Translat Neurosci (2012); 3(1): 22-7
- Martinez &amp; Milan, V Int Conf Synesthesia: Science and Art. Alcalà la Real de Jaén. España. 16–19th May 2015
- Milan et al., J Consciousness Studies, 20(1-2