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.