What could an oscillating training loss curve represent? I tried to create a simple model that receives an $80 \times 130$ pixel image. I only had 35 images and 10 test images. I trained this model for a binary classification task. The architecture of the model is described below.

conv2d_1 (Conv2D)            (None, 80, 130, 64)       640       
_________________________________________________________________
conv2d_2 (Conv2D)            (None, 78, 128, 64)       36928     
_________________________________________________________________
max_pooling2d_1 (MaxPooling2 (None, 39, 64, 64)        0         
_________________________________________________________________
dropout_1 (Dropout)          (None, 39, 64, 64)        0         
_________________________________________________________________
conv2d_3 (Conv2D)            (None, 39, 64, 128)       73856     
_________________________________________________________________
conv2d_4 (Conv2D)            (None, 37, 62, 128)       147584    
_________________________________________________________________
max_pooling2d_2 (MaxPooling2 (None, 18, 31, 128)       0         
_________________________________________________________________
dropout_2 (Dropout)          (None, 18, 31, 128)       0         
_________________________________________________________________
flatten_1 (Flatten)          (None, 71424)             0         
_________________________________________________________________
dense_1 (Dense)              (None, 512)               36569600  
_________________________________________________________________
dropout_3 (Dropout)          (None, 512)               0         
_________________________________________________________________
dense_2 (Dense)              (None, 1)                 513     


What could the oscillating training loss curve represent above? Why is the validation loss constant?
Try lowering the learning rate.

Such a loss curve can be indicative of a high learning rate. Due to a high learning rate the algorithm can take large steps in the direction of the gradient and miss the local minima. Then it will try to come back to the minima in the next step and overshoot it again. 

You may also try switching to a momentum-based GD algorithm. Such a training loss curve can be indicative of a loss contour like in this example, for which momentum-based GD methods are helpful.

I noticed that you have a very small training set. You may have better luck with a larger training data (~1000 examples) or using a pre-trained Conv network as a starting point.