In [1]: from collections import OrderedDict

In [2]: od = OrderedDict.fromkeys(range(10))

In [3]: it = iter(od)

In [4]: it.__reduce__()
Out[4]: (<function iter>, ([0, 1, 2, 3, 4, 5, 6, 7, 8, 9],))

In [5]: list(it)
Out[5]: []

This would presumably be a side-effect of all generic pickling operations of iterators; figuring out what the iterator produces requires running out the iterator. You could special case it case-by-case, but that just makes the behavior unreliable/confusing; now some iterators pickle without being mutated, and others don't. Do you have a proposal to fix it? Is it something that needs to be fixed at all, when the option to pickle the original OrderedDict directly is there?

Other iterators either don't support pickling or aren't mutated during pickling:

In [10]: it = iter({1})

In [11]: pickle.dumps(it)
Out[11]: b'\x80\x04\x95\x1e\x00\x00\x00\x00\x00\x00\x00\x8c\x08builtins\x94\x8c\x04iter\x94\x93\x94]\x94K\x01a\x85\x94R\x94.'

In [12]: list(it)
Out[12]: [1]

In [13]: it = (x for x in {1})

In [14]: pickle.dumps(it)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-14-7e86a183a31c> in <module>()
----> 1 pickle.dumps(it)

TypeError: can't pickle generator objects

New changeset a5259fb05d03f4871837c14fed704541a20896c0 by Serhiy Storchaka (Sergey Fedoseev) in branch 'master':
bpo-34574: Prevent OrderedDict iterators from exhaustion during pickling. (GH-9051)
https://github.com/python/cpython/commit/a5259fb05d03f4871837c14fed704541a20896c0

New changeset dcd56f615e89d4920a0598a9c3d3301701f238a6 by Miss Islington (bot) in branch '3.7':
bpo-34574: Prevent OrderedDict iterators from exhaustion during pickling. (GH-9051)
https://github.com/python/cpython/commit/dcd56f615e89d4920a0598a9c3d3301701f238a6

New changeset 0d3dd9fe0d2565f09f70d8ea7341dfd88e6bd380 by Miss Islington (bot) in branch '3.6':
bpo-34574: Prevent OrderedDict iterators from exhaustion during pickling. (GH-9051)
https://github.com/python/cpython/commit/0d3dd9fe0d2565f09f70d8ea7341dfd88e6bd380

Thank your Sergey for your report and fix.