Yes, in at least a couple of ways.

1) Just because you collect data on the same experimental units at different time intervals does not de facto make the design a repeated measures. A repeated measures design requires that the repeated measures be correlated. I could plant corn in the same acre five years apart and few people would like a repeated measures analysis because the soil conditions will have changed between the two measurements. Test for serial correlation before defaulting to repeated measures tests. If no such correlation exists, then revert to non-repeated measures analyses.

2) You may have encountered something like Simpsons Paradox. The addition of another variable (repeated measures variable) has enabled you to gain a clearer view of the relationship between dependent and independent variables. Unfortunately, the beautiful correlation that you though you had was an illusion generated by failing to account for all the important variables. Here is a great illustration: http://optimalprediction.com/files/pdf/V1A13.pdf. Also search for Paradox in the website ODAJournal.com.

In repeated measures design if sphericity is severely  violated then correction is applied in df to different SS due to which p value  increases resulting higher significance value. Further, if the subjects in the study does not vary much then repeated measures backfires. This might be the reason in your case. For details on repeated kindly refer my forthcoming book by Wiley titled "Repeated Measures Design for Empirical Researchers".

Best wishes

Prof. J. P. Verma

Start simple. Think of a paired t test. This increases statistical power when the repeated/paired measures are correlated positively. The variance from the correlation is removed from the calculation of the standard error and reduces it.

What happens if the measures are negatively correlated? In effect there is more variability in the differences than expected from the raw scores. This means that the variability in the differences is effectively inflated and the t test standard error larger than if the correlation was zero.

When you generalise this to ANOVA the issue becomes the whole of the variance-covariance matrix - where patterns with large  negative covariances can produce similar results. (Sphericity is also an issue, but this is a related but slightly different problem because it has to do with the distribution of the F statistic when the variance-covariance matrix is not spherical in the population - essentially in means that the variances of pairwise differences in levels needs to be identical in the population sampled for the F statistic to have an F distribution with the usual df).

A concrete real world example: litters of puppies. As puppies come from the same litter they will be correlated in weight. They compete for milk from their mother and this is a fixed resources. Bigger/stronger puppies get more milk and grow more at the expense of weaker/smaller puppies. In general you get negative correlations between puppies from the same litter there than positive ones.

In both cases - negative or positive correlations - the repeated measures analysis is the correct one.

Follow-up. One thing to watch for in some software (e.g., SPSS) is that you can enter factors as random effects rather than fixed effects. This can also mess up significance (and generally producing strange results). In a repeated measures design the unit of analysis (e.g., people) is a random factor but most software hides this from you by requiring you to set up the analysis in a particular way. The other factors tend in these cases still to be fixed effects.

Suppose that you are measuring blood pressure before and after injection of a medication. I would hope repeated measures would increase the level of significance.

However, if you are giving people a high protein diet, and have some of them exercise and do weight training, while other just exercise a lot, I would expect repeated measures to decrease significance. The reason is, high protein plus weight training=> larger muscles. 

Back when I was doing lots of cardio and weight training, my body weight went down. When I added protein, my body weight went up and % body fat went down. I was physically stronger and you could see that I had larger muscles than before. 

I would check your assumptions behind the results. I also wouldn't compare results using improper analysis methods to that of proper analysis methods. You can do a bad analysis job and "prove" just about anything.  

Be careful in checking the assumptions of the model. As an example, it is easy enough to go through the choices with the null hypothesis that the data are normally distributed, though the same logic applies elsewhere.

1) I have failed to reject the null-hypothesis.

       1a) Nearly invariably I can correct this problem by increasing sample size. See #2.

        1b) What do I do now? Having failed to reject the null hypothesis I use models that assume a normal distribution. So I am now saying that a failure to reject the null hypothesis is equivalent to proving the null hypothesis true. This is not good statistics. 

2) I have successfully rejected the null hypothesis.

     2a) I apply a transformation.

         2a-I) I now assume that the null hypothesis is true and proceed with the analysis.

         2a-II) I now retest the data to try to show that the data are now normally distributed.

  It doesn't seem to me that any of these choices result in anything other than more trouble. Choice 3 is to use a model that does not make any assumptions. Such a model does not exist. So we are left with trying several models that make slightly different assumptions and trying to extract the best approximation of truth that we can by comparing and contrasting the results. Of course, using bad statistics can enable one to lie. This is not much different than arbitrarily selecting what we think is the appropriate model and going with whatever it seems to tell us.