The short answer is that what you are asking about doing is routinely done in psychology and sociology research. In fact this approach has even been published with the BFI-44 specifically:

http://www.sciedu.ca/journal/index.php/jnep/article/viewFile/1348/1205

It's in a journal I have not actually heard of, but the authors display more sophistication regarding CFA than I am accustomed to seeing in many mainstream psychology journals.

However.....

When you modify the scale based on statistical criteria alone you have to be concerned about  fitting noise and quirks in the data rather than meaningful phenomena. As such, you would ideally validate any changes made on statistical criteria alone in an external data set. That being said, this validation step is often not actually done (the above article did not do it).

The short answer is that what you are asking about doing is routinely done in psychology and sociology research. In fact this approach has even been published with the BFI-44 specifically:

http://www.sciedu.ca/journal/index.php/jnep/article/viewFile/1348/1205

It's in a journal I have not actually heard of, but the authors display more sophistication regarding CFA than I am accustomed to seeing in many mainstream psychology journals.

However.....

When you modify the scale based on statistical criteria alone you have to be concerned about  fitting noise and quirks in the data rather than meaningful phenomena. As such, you would ideally validate any changes made on statistical criteria alone in an external data set. That being said, this validation step is often not actually done (the above article did not do it).

The fact that it's an established scale makes little difference to the question, in my opinion, from the methodological perspective. Though it may make quite a large difference in the peer review process. Bear in mind that many established scales became so before rigorous measurement evaluation became widespread (even if you consider it widespread now).

To answer the general question, I agree with Paul's answer that there's a serious risk of overfitting.

Pat

In case cross-validation with an external data set is not possible, as indicated by Paul Gerrard before, it might be worthwhile compare your items (and what they capture) with other, shorter Versions of the BFI. There's a 10-, 15- and a 21 item Version of the BFI, that have been published:

Rammstedt B, John OP. Measuring personality in one minute or less: A 10-item short version of the Big Five Inventory in English and German. Journal of Research in Personality 2007;41:203-12.

Gerlitz J-Y, Schupp J. Zur Erhebung der Big-Five-basierten Persönlichkeitsmerkmale im SOEP - Dokumentation der Instrumentenentwicklung BFI-S auf Basis des SOEP-Pretests 2005. DIW Research Notes2005.

Rammstedt B, John OP. Kurzversion des Big Five Inventory (BFI-K): Entwicklung und Validierung eines ökonomischen Inventars zur Erfassung der fünf Faktoren der Persönlichkeit. Diagnostica 2005;51:195-206.

I think Paul Gerrard's advice is good. Scales are developed, in part, using statistical criteria (such as corrected item-whole correlations and factor analysis). But it is not uncommon for some items to "deteriorate" in future samples: no longer to perform as intended. This may be owing to features of the new sample, as in the example Dr. Gerrard submitted a link to. (Those researchers were using the instrument in a Chinese sample to see how it worked.) It can also be produced by "drift" in the meaning of the item over time. Or just by carelessness or bad luck in the original development.

So feel free to remove items that do not load on the appropriate factor. But be up-front about the fact that you have done so. And above all, do so based on the statistical properties of the items without "peeking" to see what impact this has on your results. Because after all, you're interested in how well the traits correlate with some other criterion. It would not be okay to just remove items that don't correlate with your criterion variable.

I would also consider some of the limitations of CFA in capturing FFM traits accurately given the over-constrained nature of the CFA model (i.e., that none of the latent factors are correlated without model based corrections- which should not be necessary). This is part of the reason that there has been some emphasis on CFA not being the best analysis for validating FFM instruments.

Keeping this in mind I would caution you against removing items based upon poor CFA fit given their restrained nature. I would suggest instead exploring the model either through an EFA or a ESEM analysis to ensure that the item is not good but belongs elsewhere. CFA makes a ton of dangerous assumptions given the oblique relationships which exist in personality. Brown (2006)'s book on CFA makes explicit and repeated point of this for FFM research.

For more on the limits of CFA and alternative analyses, see:

(a) Booth & Hughes (2014) Exploratory Structural Equation Modeling of Personality Data

(b) Gignac, Bates, & Jang (2007) Implications relevant to CFA model misfit, reliability, and the five-factor model as measured by the NEO-FFI

(c) Marsh, Nagengast, & Morin  (2012) Measurement Invariance of Big-Five Factors Over the Life Span: ESEM Tests of Gender, Age, Plasticity, Maturity,

and La Dolce Vita Effects

(d) McCrae et al (1996) Evaluating Replicability of Factors in the Revised NEO Personality Inventory: Confirmatory Factor Analysis Versus Procrustes Rotation

Thank you all so much for your very valuable advices and the suggested literature! I think, I have a plan now! :)

Hi Charlott

A bit late....but perhaps item 'parcelling' is a viable alternative to excluding items and running the risk of making sample specific modifications to your scale; although parcelling in itself has both strengths and limitations that you should be aware of.

Little, T. D., Rhemtulla, M., Gibson, K., & Schoemann, A. M. (2013). Why the items versus parcels controversy needn’t be one. Psychological methods, 18(3), 285.

Little, T. D., Cunningham, W. A., Shahar, G., & Widaman, K. F. (2002). To parcel or not to parcel: Exploring the question, weighing the merits. Structural equation modeling, 9(2), 151-173.

Matsunaga, M. (2008). Item parceling in structural equation modeling: A primer. Communication Methods and Measures, 2(4), 260-293.

Yes you can. Please check Hair et al.'s Multivariate Data Analysis (Seventh Edition) or LISREL Modeling by Anderson and Garbing.