This is the expected result. We can be much more certain about the terminal nodes of the tree than we can be about the tree's deep structure, trivially (but not exclusively) because of uncertainty propagation from the tips down into the internal nodes (a deep node is only as good as all of the nodes that lead to it). You can see a similar phenomenon in the various phylogenies in this classic paper.
It is also possible that your gene is not variable enough, not just that it is too variable. If there is a subset of highly informative positions in your gene, bootstrapping samples that miss those positions would be expected to yield noisy results.
In terms of how to resolve these, the traditional answer is "more data". This data can come in either the form of more species/tips or more sequences per species (ideally both). It is probably unsurprising that you aren't able to get very confident with a single gene. Even a rather older approach uses 31 universally conserved genes. As is traditional in statistics, we get more certain about our estimates as we use more data to arrive at them. In these methods, the genes (proteins) are indeed concatenated.
Note also that single gene trees can be positively misleading about the true phylogenetic relationship, due to incomplete lineage sorting or other such phenomena. In this case, you could have excellent bootstrap support for a wrong phylogeny.
In another paper, you will find the following statement:
In molecular phylogenetic analysis, it is often the case that some relationships are robust, and relatively "easy" to recover while others are difficult to resolve, leading to phylogenetic hypotheses that consist of a patchwork of well and poorly supported nodes. When difficult nodes are encountered, the next logical step is to add taxa and/or data under the reasonable assumption that additional taxa or characters might enable resolution and/or provide support for poorly supported nodes...
The amount of data required for resolution of difficult phylogenetic problems associated with short internodes, especially those deep in a tree can represent a particularly difficult challenge [5–7] that often requires massive amounts of sequence data to resolve.
Deep nodes are just harder than shallow nodes! The possible exception here is the very oldest splits, where enormous amounts of evolutionary time might separate outgroups quite clearly from a relatively messy subtree (see the Fishbein paper for more examples of this).
