Using a criteria of an eigenvalue greater than 1 is not always a great way to determine the number of factors that should be retained in an exploratory factor analysis. I would suggest you consider also examining the Scree plot, as well. Also consider the total amount of variability in all 15 items accounted for by a two vs. a three factor solution. It is a combination of factors and not a single cutoff value that should inform your decision. Also, you should consider whether there is any theoretical reason to expect two vs. three factors.  

If you would like a more empirical basis for determining the number of factors to retain, rather than weighing multiple related pieces of information, you could use Horn's Parallel Analysis. The article I link below provides instructions using SPSS or SAS. There are also easy to implement options in R using the nFactors package. 

https://link.springer.com/article/10.3758%2FBF03200807?LI=true

http://www.statmethods.net/advstats/factor.html

Thanks a lot Matthew, that was helpful

Dear Rohit,

When you say "loads" I presume you are referring to loading greater than a predetermined cutoff value, such as 0.3 or 0.4. Depending on your sample size you should seek a certain minimum number of items loading on each factor above a certain cutoff value. One item is clearly unacceptable, so is 2 as each factor must contain at least 3 items. One study suggests at least 4. You also need to be aware of cross loadings. It is the ratio of loadings which should be considered, e.g. 4:3. Please see my article on reliability analysis with small samples.

Correction- I mean my article on exploratory factor analysis.

"I know implicitly that this particular variable is an outlier, and doesn't particularly belong as a third factor in the model."

Theory rules, and statistical models are mere attempts to make sense of things.  A problem though is that you are making this decision after seeing the results.  In a perfect world the outlier variable would have been eliminated a priori, perhaps because alpha is lower with it in than without it, and you would have got a simple interpretable 2 factor solution.   But since it wasn't deleted, I think you should delete it now (I agree with others that a 'one variable factor' is problematic) report everything you did completely transparently, making the combined theoretical and statistical argument for deletion and opting for the 2 factor solution.  Then when discussing 'future research' you could speculate whether there could be a third latent factor out there that would be discoverable with more variables, and if so what that factor is and how it would fit with the rest of the theory.

Thanks to everyone for this insight. Sometimes its easier to ask questions than to get stocked at points like this