Hi there,
Negative loadings can mean a few things. First, you should consider whether or not the questions make sense and are theoretically grounded and you can justify keeping the question(s) in the final scale. Sometimes questions can take away from the overall scale and 'make things worse' so to speak. If your factor with negative values has less than 3 items on it, I would remove the scale (check your eigenvalues and all other appropriate statistics before, but generally a good rule of thumb is if your scale has 3 items or less it doesn't contribute that much to the grand scheme of things).
Second, and what may be a better option for you, is that the questions need to be reverse scored in the final measure. If your negatively-worded questions are giving you a negative value when you reverse score them I would encourage you to step back first. As factor analysis is statistically driven and your initial wording and working theory is not, I would recommend running EFA or PCA on the data prior to doing any recoding or negative coding on any of the data. When you have the results from the analysis you can determine if the questions are supposed to be reverse scored or not.
Example: A 10-item measure, you run PCA. You get 10 factors (expected), but only the first 3 have eigenvalues above 1.0. Factor 1 has weights of .386 - .586, factor 3 has weights of -.389 through -.876, and factor three has 4 items with weights of .580 - .678. Keeping in mind the balance/greatest weight of the item is the factor to which it applies, read over the data. The items in factor 2 may need to be reverse scored. Try reverse scoring the items on factor 2 and then run a confirmatory factor analysis and determine the results.
Food for thought: I ran in to this issue multiple times (more than I should ever care to admit publicly....) when I was making a new measure for a construct that consisted of 45 items. What I did was run principal components analysis (PCA, which is different from factor analysis) and determine the number of latent variables I had. I kept anything that had eigenvalues above .7 and any item(s) with a weight of less than .300 were discarded. After running the PCA I ran a confirmatory factor analysis (CFA). PCA asks 'What is the underlying structure I have here?', which in my case PCA said 'You have 3 factors that relate to your construct.' CFA says 'Hey, PCA said this. Was he right?', which in my case CFA said 'Yeah, pretty much. Here are the stats to prove it.'
Tip: SPSS doesn't do confirmatory factor analysis. If you are using SPSS I recommend using it for the PCA because the output is much nicer and you can do more rotations in SPSS than you can in other programs (if you need rotations at all). Once you have your underlying factor structure from your PCA run a CFA using Rcmdr. Rcmdr is an R plugin and is completely menu-driven so no coding experience is necessary. The output is very easy to interpret, setting up the analysis is easy, and all of the necessary statistics are given to you when you run the analysis (plus more).
I'd be happy to help if you wish, feel free to message me if you would like.