Usually the factor loadings have the same signs mainly beacause they indicate the statistical association among observed variables (items) and a latent variables (or latent variables in case of a second order construct). Hence, the items are the "indicators" of the latent variable: if you have a negative sign I would suggest to delete that item because maybe it is correlated/related to another latent variable of your model.
It is very important that you firstly conduct an exploratory factor analysis (EFA; a PCA for example) to see if the items of a single factor (component) are actually related, positively or negatively, to that variable. After these exploratory analysis you should conduct a confirmatory factor analysis (CFA) which is what you were doing I guess. At this point try to compare the fitting indexes (both absolute and relative) of your CFA models with and without that negatively associated item: I'm quite sure you'll have better fit with the model showing only positive factor loadings (same signs!).
Ok, my feeling is that maybe the negatively associated indicators were a reverse item, is this the case? If so, reverse/re-code it.
Another query: are you using a validated scale or are you attempting to validate your own scale?
In the former case, you'll find all the answers in the validated paper/study you've used.
In the latter case, an EFA is necessary and it'll show you the items' weights of association in relation to your latent variable. Moreover, try to delete during your EFA the negative items to see if your % explained variance increases or decreases. Finally, conduct a CFA to see how it all works with or without those negative items.
Everything depends on the theory you're using, if it "makes sense" to have negative related items, it could be ok (but pay attention to that and compare your findings with the existing pertinent literature!).
I suggest you to have a look at James Gaskin's videos/tutorials which helped me a lot to better understand EFA/CFA with AMOS: https://youtu.be/JkZGWUUjdLg