If the actual change is large relative to the unexplained variance, then you will need fewer data to declare "significance".  If the actual change is tiny compared to unexplained variance then you will need a lot more data.  Although two points is all you need to connect a line, you still won't be able to tell there is real change or just random fluctuation.  Typically, a power analysis is done to inform the amount of data you should collect.

The sensitivity of your conclusions about change to the sample size you happen to have should cause some contemplation.  See Johnson's (1999) classic paper on "The insignificance of statistical significance testing" (Journal of Wildlife Management) and the recent special edition of Ecology vol 94, 2014 on the use of P-values.  

I think a key thing to note is that null hypothesis testing of "change" isn't very meaningful until it is placed in a broader context (most things in nature are inter-dependent, so just get enough data!).  To this end, see Dixon's (2005) paper in Ecology on "A statistical test to show negligible trend" or consider a Bayesian analysis that yields the probability density of different magnitudes of change supported by your data, given your prior belief about change.  Ideally, you would have multiple competing models of what is driving change in veg cover, and then use AIC or it's variants to evaluate the relative strengths of these models (see Burnham and Anderson 2002 book titled; Model Selection and Mulltimodel Inference).

In a repeated measures analysis, the number of temporal data points you want to collect depends on the type of the function you are hoping to find.  For a linear dependency, two temporal datapoints collected from a sufficient number of sites may be enough.  If the dependency you are looking for is exponential, six points may be enough.  If the phenomenon is cyclical, you will probably need at least 10 points within one period.  This is really your call, at the end of the day.  Simply imagine a line on the graph that you hope to find -- and then ask yourself: how many points do I need to put on the graph so that when I connect them all with a marker, the line looks like what I am trying to find -- after I take into account the amount of measurement error I am prepared to tolerate in my picture.

If the actual change is large relative to the unexplained variance, then you will need fewer data to declare "significance".  If the actual change is tiny compared to unexplained variance then you will need a lot more data.  Although two points is all you need to connect a line, you still won't be able to tell there is real change or just random fluctuation.  Typically, a power analysis is done to inform the amount of data you should collect.

The sensitivity of your conclusions about change to the sample size you happen to have should cause some contemplation.  See Johnson's (1999) classic paper on "The insignificance of statistical significance testing" (Journal of Wildlife Management) and the recent special edition of Ecology vol 94, 2014 on the use of P-values.  

I think a key thing to note is that null hypothesis testing of "change" isn't very meaningful until it is placed in a broader context (most things in nature are inter-dependent, so just get enough data!).  To this end, see Dixon's (2005) paper in Ecology on "A statistical test to show negligible trend" or consider a Bayesian analysis that yields the probability density of different magnitudes of change supported by your data, given your prior belief about change.  Ideally, you would have multiple competing models of what is driving change in veg cover, and then use AIC or it's variants to evaluate the relative strengths of these models (see Burnham and Anderson 2002 book titled; Model Selection and Mulltimodel Inference).

A power analysis to see what the sample size should be to detect the effect you're looking for, and this would help to explain your conclusions; oh, I just noted its in the above reply. However, you could also see from your sample size what type of power your analysis/conclusions have.

Matt / Shawn, the question Mahyar asked was not about the proper sample size, but about the number of repeated measurements for each entity within the sample -- that is, assuming the sample size is enough to find a significant difference, even for two measurements: "before" and "after".

Maybe Mahyar can elaborate on the question and design if I've misinterpreted him.

See this discussion about using the same dataset for deriving conclusion and as well as performing a "post-hoc power analysis". https://www.researchgate.net/post/Is_it_possible_to_calculate_the_power_of_study_retrospectively 

I think there are a lot of good argument and references provided that argue against doing post-hoc power analysis.

My suggestion assumes more that Mahyar meant what majority of the earlier followers answered than not. Assuming you do not wish to conduct a pre-power analysis to inform the amount of data to collect, and since you may not readily infer large changes relative to the unexplained variance at an unassuming stage of your work, I suggest you collect replicate data sets from each of your sampling points to make your data sizeable enough for meaningful results.

You may also apply other related statistical models that could capture latent relationships that linear models alone can not capture. Depending on your data set, Hierarchical Cluster Analysis (HCA) could help.

However, recall that even results that reveal "not significant" are also reliable and revealing in research.

Thanks a lot Alex for the answer, however, what I meant was understood well by Matt and Shawn. My concern is to make sure how large my sample size should be in order to produce a meaningful result, based on the context of my research. My ultimate is then to explore the function, which fits the best to my data set, I am not assuming a specific function type in advance. 

To Matt: I am grateful for the references. They were really helpful and relevant to my concern. If I am not wrong, there is no way to ascertain the sufficiency of sample size, unless the results are out and the variation is known!?    

Yes, Mahyar, I believe you are correct.  You would have to use literature review to determine an appropriate variance to use in the power analysis, and you would also have to supply an effect size.  I know this is not very satisfying.  Incidentally, the Journal of Basic and Applied Social Psychology has apparently banned p-values from their journal.  They also banned confidence intervals, which is a little like tossing the baby out with the bath water in my opinion.  Null Hypothesis Statistical Testing is contentious, and academic statisticians are often in disagreement about how to best quantify "evidence".