As Greg87 and IRstuff point out, DI and Distilled are very different.
Distilled is a simple boiling/vapor condensation process which does not remove similar boiling point volatiles nor does it eliminate dissolved oxygen and CO2. Both of which are "terminal" when it comes to a high purity situation.
Water purity is best identified using resistivity or conductivity ( they are exact inverses ).
The most pure condition available with current technology is 0.055 microSiemens or about 18 MegOhm water. Essentially, water without ions.
However, the although the purity of water remains unchanged, its conductivity is dramatically affected by temperature.
Take 18 MegOhm water at 0C. It will become 5 Megohm water at 50C. Without any contamination whatsoever.
Add 20 ppm of NaCl and it will become 1 Megohm water.
Temperature and contamination are the concerns.
Materials of construction and elimination of ambient gas contamination by Oxygen and CO2 are other concerns.
DI water "wants" ions because it has none. The driving force is tremendous.
Distilled water has a resistivity of 100K ohm to 1 Megohm.
DI water is 5 to 10 times that value.
The point here is produce what you need and use it fairly quickly. If DI water stays around it will become contaminated. Sure, DI resin beds can keep it deionized, but if your piping system is metallic and/or there is oxygen present, then you will fail to keep it DI.
Good luck.