How to save/fix the column width in the Nemo file manager?

Update Nov 2016: Solution for 16.04 and following versions (No solution for Xubuntu 14.04): A patch with a work around has been added to Nemo: the non-name columns should start out at their natural minimum size, with the name column expanding to fill the remaining space, see github forum. Nemo 3.2 with unity patches was added by Andrew (THANKS A LOT!) to webupd8.org PPA Nemo3:

sudo add-apt-repository ppa:webupd8team/nemo3
sudo apt-get update
sudo apt-get install nemo nemo-fileroller

Update Sept 2016: More info please, see webupd8.org PPA Nemo 2.8.7. He could not patch Nemo 3 for Ubuntu (with Unity):"Unfortunately I couldn't update Nemo to v3, it requires so many updates to the old patches that I doubt anyone will do it. However, I did manage to include the list-view patch, as well as some other patches from Nemo 3, into Nemo 2.8.7. Those patches seem to only work with GTK 3.18 and newer (I'm not sure, but I saw in a commit that they need some fixes to work on Linux Mint 17.x and thus, Ubuntu 14.04). That's why I uploaded Nemo 2.8.7 with these new patches for Ubuntu 16.04 only."

Update January 2016: No new feedback since May 2015, please leave a comment in the github forum to encourage work on this. Thanks.

May 2015: There is no possibility to do it at the moment unless you compile it yourself (see below).
But there is hope, mtwebster wrote:
"There is a large history behind this issue - it's definitely not uninteresting, but there's not an easy fix that pleases everyone - it's a no-win scenario.
Brief timeline: Nemo remembers list view widths. People complain they can't reduce widths of some columns to fit a useful list into a small window, and hate having horizontal scroll bars.
We try to accomodate and make columns able to be made very small if desired. Oh, but Gtk got changed in the mean time, and the list view class we use is actually now broken and we're unable to implement this. You can resize as much as you want, but you never get a horizontal scrollbar, ever. So columns just disappear if you make other columns too wide. The Gtk change also means we can't even go back to the way things originally were - we're on an island.
The current behavior is implemented as a temporary fix until we figure out what to do.
We patch the gtk we ship with Mint to 'band-aid' the problem (actually a rejected patch someone submitted to the Gnome devs). There's a PR (#611) to restore the original behavior (see list item 1). This of course will only be useful to people that liked the original behavior, but doesn't improve anything, and only applies to those running this patched Gtk (Mint 17 users).
You are here.
So, yeah it's been kicked under the rug a bit, and that's our fault. But there's not been a clear solution either. I'll take a look again in the next couple weeks if I can fix the issue at hand here - remembering widths - before 2.6."

A possible but difficult fix:
A primitive workaround at least to start nemo with increased "name" column width is to modify nemo-list-view.c:
gtk_tree_view_column_set_min_width (view->details->file_name_column, 125);
into
gtk_tree_view_column_set_min_width (view->details->file_name_column, 300);
Because that is a 'c' source file, although it is just accessing an API, so could be written in a script language, it is not, so you would need to get all the other sources, and compile them with the right settings then replace the executables, and repeat the whole thing each time nemo was updated.
Source: Github Forum

Just my two cents but after I installed the fileroller I had the same issue.

However, when I ticked the option

ignore per-folder view preferences in prefs > behaviour

I could resize the columns & it would remember them.

Obvs per folder didn't matter, but at least I could set the size of a column such as the name & it seems to remember it across sessions :)