Hello.
First off all take a look at the pictures I attached bellow. I never had this problem before. Probably the soil is the one giving me the problem.
I am writing about a 2yrs old Tahiti lime from cutting. I've been growing citrus for a while now and this is the first time I have seen this.
This tree refuses to grow its new fruits. During the summer it flowered several times and most of the fruits dropped. But most of them just stay for 2-3 months there. They won't grow or drop. I must mention that on the tree there are 2 limes since last winter.
I fertilize it every 2 weeks, water it constantly, no bugs on it, full sun for 3-4 hours/day. Also I didn't see a flush for a while and the last one (2.5 months ago) was spindly. Last month I have seen some spider mites on it, but I got rid of them fast.
Some suggestions would be nice.

Probably a lack of sun, 3-4 hours is not enough for good fruit production. Increase the hours of sun and you will increase the amount of fruit. All my trees get about 10 of direct sun and carry tremendous amounts of fruit for there size. Your tree is probably carrying as much fruit as it can. Ill post a image of my Tahiti lime which receives 10 hours for comparison soon.

Probably.. Though I tend to disagree.

Three reasons:
-Until one month ago it had 4 mature fruits on it. In the meantime I removed 2 of them (I was having your opinion). Nothing happened... the new fruits didn't change in size. The ones in the picture are 2.5 month old.
-I have grown citrus before. 3-4 hours of full sun (and the rest of the day partial sun) is more than enough to have a nice crop. Even this tree fruited last winter with no sun.
-The tree should have dropped all/ most of the new fruits and decide how many to grow (in 2.5 months even a tree can take a decision).

Something else is happening. It lacks something or has it in excess.

The soil is either too dry , or the key element = fertilizer doesn't get inside the tree , many can cause something like this , Ph level si one of them . The aiir is maybe too dry , or maybe it is rootbounded already
I would go for a soil problem dough.
There is a thin line you can walk on regarding citrus trees.

Good Luck to you and to your trees

maybe you temps are too low? you say you fertilize every 2 weeks, at PPM? PH? NPK ratio? no bugs.

Soil problems tend to show different symptoms, your trees look healthy, other then kind of spindly form lack of sun.

It is also a well known fact that citrus carry more fruit when exposed to more hours of sun. I still think this is your fundamental issue. I bet if you exposed this tree to 8-10 hours it would fruit much more and become more dense with foliage.

Ryan, could certainly be correct (and probably is) about additional sunlight. However, it all depends. Light is the only source of energy for a citrus tree. The tree uses light to manufacture photosynthates (the tree's food). That said, it should be pointed out that citrus are low light plants. A citrus tree maximizes its production of photosynthates at 650 PAR (Photosynthetically active radiation) which is only 1/3 of full sunlight. Higher levels than 1/3 sunlight will not produce more food for the tree. Only longer periods of light will keep the tree producing additional photosynthates. So it all depends on the quality and quantity of light covrig's tree is receiving when it is not receiving full sunlight. As far as pH, it could possibly be the cause the tree's problem, but I really doubt it, as a citrus tree will produce a good crop of fruit at a pH anywhere between 6 and 8+. - Millet (524-)

Millet, Good point about PAR but, normal shade will reduce PAR, If you reduce sunlight in effect you reduce PAR. There must be some type of coverings(greenhouse glass/plastic) that can filter out wavelengths other then PAR but we don't not known in this case.

Here is my Tahiti(also knows as Bearss) lime tree about the same age as yours around 3-4 years, it receives about 10 hours.

My tree is 2 yrs old. I wanted to keep it small, hence the small pot. I don't have enough space to keep all my plants so I need to either give some away or to keep them small.
It isn't about the light. I have enough for a citrus tree. It isn't inside as you can see. It isn't about the light because last winter it has grown its fruits without a problem (and we have harsh winters here).
I had a discussion with danero2004 and probably the plant has some problems with the root system. The lime tree can't grow enough small roots to absorb nutrients. I will leave it like that for one more month then I will change the type of soil.
Regards.

If you are convinced its the soil, remove the root ball and inspect. this will answer the question quickly, post a picture if you do.

Ryan, yes, as you say there are variables. Full direct sunlight is 2000 PAR. A citrus tree maximizes food production for itself at 650 PAR, which is only about 1/3 of full sunlight. Originally, citrus in its native habitat, grew as under-story trees, beneath the shade of the taller forest. Without knowing the quality and quantify of the light that covrig's tree is receiving when not in the direct sunlight I would certainly lean toward your assessment. The tree does look rather spindly, but on the other hand all of the growing energy required by the fruit to grow, and mature, will come only from the fruit's closest three leaves. All in all, I cast my vote with Ryan. - Millet (523-)

I agree with Millet this time could be a possibility that the tree indeed does not have enough leaves to proper feed the fruits still a a good root ball is necesary in order to produce some fair leaves , and viceversa fair leves lead to good root ball

I don't think there's anything wrong with your tree - you just aren't patient enough!
However, I would cut off all but one of the tiny fruits so that the remaining one gets all the nutrition. The presence of near-mature fruits probably doesn't help either, so harvest them as soon as possible.

Just out of curiosity since some of you guys mention energy towards fruit production. Wouldn't that be infinitesimally small given the size of the fruitlets?

If the tree really has stopped growing my guess is also a lack of light, I had a jalapeno pepper plant do the same thing - fruits everything stopped growing mid growth (was an indoor plant). It does seem that plants store up some energy so the effect of a lack of adequate light (or not enough PAR) is latent to some degree - in other words you don't notice the effect on the plant for some time.

Catalin,
Could be possible that the pot become to small for the roots, no space for new roots, your tree goes in ‘stand-by’.
As RyanL mention above check the root ball.

Stoddo, concerning the question you ask above about the infinitesimally small fruits and energy stopping growth, see link below about what stops growth. - Millet (520-)

link