The recent downtrend has been motivated by the significant increase in probability of an upcoming FED rate hike in either June or July. As long as this forecast keeps being valid the EUR should continue to loose ground to the USD.
However, the fact that the FED's decision is so close in time could put a halt to this development due to the natural uncertainty leading up to the mid June meeting. The upcoming 6th of June speech by Mme Yellen will certainly provide some degree of insight on this possible move's chances.
A rate hike in June could potentially even break the low 1.05