Q:

'the fact that'

I used the following sentences having a statement of 'the fact that'
Original sentence:
1) The effectiveness of MDPs for low-income women has been supported by the fact that women’s microenterprise has significantly increased their incomes, empowered them to gain autonomy in their family as well as improved the welfare of their families and children. 
2) the fact that the addition of the social capital variables significantly increases the power from Model 1 to Model 2, 3, and 4 implies that social capital also contributes to the relationship between gender and business start-up.  
A reviewer of a journal asked me to eliminate 'the fact that'.  Is using 'the fact that' reduntant?  Could you give me alternative sentences not having 'the fact that'? 
What about 'despite the fact that'?  Instead of this sentence, do I need to use 'although' to avoide using 'the fact that?' 
Thank you so much in advance.   

A:

It's not redundant.  It can though become heavily used, and it is almost always possible to rephrase into something snappier, or at least which doesn't use the phrase repeatedly (more or repetition later). 

The effectiveness of MDPs for low-income women has been supported by women’s microenterprise significantly increasing their incomes, empowering them to gain autonomy in their family as well as improving the welfare of their families and children. 

In doing this, I fixed "as well as improved" which I didn't even notice as a flaw until I came to the edit, and clearly neither did you. 
It's not a big improvement, but it is marginally better IMO. 

The addition of the social capital variables significantly increasing the power from Model 1 to Model 2, 3, and 4, implies that social capital also contributes to the relationship between gender and business start-up. 

Again, not a great improvement, but a slight one. 
I'd say they'd be even greater improvement if you use the phrase a lot.  Repetition is often overly worried about by some writers, and some questions here will be about trying to avoid repeating small words like of or pronouns and such a concern is probably mistaken; heavy avoidance of repetition tends to lead to strange and unwieldy phrasing.  However, larger phrases can grate if you repeat them and idioms like this can be particularly at risk. 
"Despite the fact that" is if anything more dangerous in this regard.  It's easy to fall into the trap of using it so often that by the end of an essay or article the reader's mental voice is one of a mocking sing-song as they come across yet another "despite the fact that". 
In collaborative or anthologised works, are publications like magazines and newspapers where you've pieces from several writers, there's a further risk; you've only used the phrase once, but the reader has just read half a dozen other pieces that used it, so the effect is that of tired repetition, though you are not fully to blame. 
There's nothing technically wrong with it, it can just feel a bit tired, so it's a reasonable style decision for your editor to prohibit it. 
If anything, the danger comes from it being too useful, because it does come naturally when putting your thoughts about the relationships between different things down on paper, and that is precisely what leads to it being overused.  It's a good thing to consider killing whenever you are re-drafting. ( A quick google search finds a lot of places where I've used it on this site, which if anything reinforces the idea that it can easily become over-used). 
Finally, it doesn't really add anything over the alternatives.  One could justify "the very fact that" as at least having a greater emphasis, but I know I personally over-used that one in first-draft writing too!