This is definitely a common situation. I wouldn't say "normal" because there is no "normal". The ratio of designers to developers is a direct product of how highly design is valued by management. I once worked in an organisation where, and I'm not exaggerating, there were 80 developers and testing staff, and I was the only designer. Trying to effect change was nigh impossible because of the political environment, and eventually I left when I realised that I could only do so much.
However, just because your situation is a common one doesn't mean that you can't be more effective, and eventually change the culture of the organisation to get more support. Here are a few ideas that come to mind:
* Get buy-in from higher up. This is probably the biggest opportunity to effect change. When research and design are undervalued, it usually stems from the top. If you can convince someone higher up that research and a robust design process will save money in the long run, then that will filter down, resulting in you having more time to do research and evolve your process, and the organisation investing in more designers.
* Be more transparent about what you do. If you can show artefacts that work in progress, then people around you will realise the value you're adding. It may be tough, but if you're able to create a design wall where you can post wireframes, concepts, user flows, personas and other artefacts, then others will look at it, comment on it, and want to share their opinion. These conversations will make design more collaborative and take the pressure of you to be the "expert". Another way to be transparent would be to share a highlights reel from usability testing sessions at meetings. There's the risk that people will respond with "but that's your job to fix" but if your managers are astute they will realise that it's impossible for one resource to manage iterative design changes as well as work on new features, all across multiple projects. Plus watching a user fail evokes strong empathy and will make people realise how important something like usability is.
* Educate and empower your team to make design decisions. If there's no additional design resource in site, you may need to resort to training your developers to make some basic design decisions, to free you up to work on more complex design challenges. I don't know your situation, but suppose you were to run a series of "brown bag" lunchtime design workshops over a series of a few weeks, so that developers become empowered to make basic layout decisions, or even run usability testing sessions. You could also distribute copies of books like Steve Krug's Don't Make Me Think or Jeff Gothelf's Lean UX onto desks for people to read. Another option for encouraging an interest in design is to link to case studies and other interesting articles on the intranet or by email. The collection of Zurb quips is a useful place to start.
* Try and involve your team members in design. Taking this one step further, you could try having team members be more involved in design by running collaborative design sessions, running some design games to encourage creativity, and becoming more of a design facilitator than a designer. One easy way to do this would be to have stakeholders, developers, or managers participate in usability testing sessions.
* Get better at scheduling your time, and be up front when managing expectations. If the issue for you becomes one of your own capacity, rephrase what you've been asked to do in terms of priorities, and put the decision back on your manager. If they come to you with something "urgent", explain to them that it may be possible for you to complete that task, but also explain what it is you're currently working on, and how much those tasks will be delayed, them ask them to clarify whether they're OK with those tasks being delayed by that much because of this one urgent task. It's likely that one task may not be quite so urgent any more...
I'm sure other folks will have suggestions, but hopefully that's helpful as a start.