No, I don't think you should be concerned. Here's an example.

R squared must be increasing, but because of precision, you might not be seeing it.

First generate some data:

library(MASS)
sigma <- matrix(c(1.0, 0.8, 0.8, 0.4, 
                  0.8, 1.0, 0.7, 0.4, 
                  0.8, 0.7, 1.0, 0.4,              
                  0.4, 0.4, 0.4, 1.0),nrow=4)

d <- as.data.frame(mvrnorm(Sigma=sigma, n=2000, mu=rep(0, 4)))
names(d) <- c("y", "x1", "x2", "x3")

Run two models, one with one additional predictor.

> model1 <- lm(y ~ x1 + x2, data=d)
> model2 <- lm(y ~ x1 + x2 + x3, data=d)
> summary(model1)

Call:
lm(formula = y ~ x1 + x2, data = d)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.76599 -0.32031 -0.00252  0.31977  1.58157 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 0.008183   0.010902   0.751    0.453    
x1          0.475810   0.015359  30.980   <2e-16 ***
x2          0.470222   0.015263  30.808   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.4873 on 1997 degrees of freedom
Multiple R-squared: 0.7615, Adjusted R-squared: 0.7613 
F-statistic:  3188 on 2 and 1997 DF,  p-value: < 2.2e-16 

> summary(model2)

Call:
lm(formula = y ~ x1 + x2 + x3, data = d)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.6898 -0.3148  0.0086  0.3269  1.5480 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 0.007822   0.010861   0.720    0.471    
x1          0.464192   0.015573  29.808  < 2e-16 ***
x2          0.460004   0.015417  29.837  < 2e-16 ***
x3          0.048184   0.012008   4.013 6.22e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.4855 on 1996 degrees of freedom
Multiple R-squared: 0.7634, Adjusted R-squared: 0.7631 
F-statistic:  2147 on 3 and 1996 DF,  p-value: < 2.2e-16 

In the first model, R-squared is 0.76, in the second model, R-squared is 0.76, but the p-value on x3, which was added in the second model is highly significant.

You can test the change in R-squared with the ANOVA command:

> anova(model1, model2)
Analysis of Variance Table

Model 1: y ~ x1 + x2
Model 2: y ~ x1 + x2 + x3
  Res.Df    RSS Df Sum of Sq      F    Pr(>F)    
1   1997 474.26                                  
2   1996 470.46  1    3.7953 16.102 6.223e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

The p-value is the same as the p-value for x3 in the second model. The change in R-squared was small, but it was significant. That can happen, it's not a problem.